Bran Stark and Jon Snow don't cross over very often in Game of Thrones, but their destinies are bound to one another, perhaps more than anyone in the Stark family. House of the Dragon has demonstrated the importance of the strength of a household and Jon and Bran are a great example of the benefits of that bond.
The two brothers (or actually cousins) might have one of the best relationships in the show, considering they continue to look out for one another even from afar. Bran always appreciated the role Snow would play after all, and, in return, Jon has always sought to protect the younger heir to Winterfell.
"Your Grace. I'm Sorry I Wasn't There When You Needed Me."
Jon Snow - Season 8, Episode 6
Jon Snow always tried to look out for his siblings. Despite everything he has done for Westeros, he held a real guilt with him, suggesting that he hadn't acted perhaps how he should have done. He was never there when it mattered most in his own eyes.
That extends to his protection of Bran. As one of the youngest members of the Stark family, he would have sacrificed everything to protect Bran and indeed eventually did, demonstrating how strong their connection was. He's happy to bend the knee to Bran so easily too, placing his ego to the side.
"You Were Exactly Where You Were Supposed To Be."
Bran Stark - Season 8, Episode 6
Bran Stark is always one step ahead, having a much deeper understanding of the future than those around him. When Jon Snow suggests he wasn't able to help him when he needed it, Bran is simply able to tell him that he was where he needed to be.
It's a reassurance that Jon appreciates, and it showcases that Bran always sees the bigger picture. Bran has learned from the mistakes of the past and is willing to support his family for the greater good. He isn't bitter as someone like Sansa might be, that he was left behind by Jon, understanding his duty.
"I Wish I Could Be Here When You Wake Up."
Jon Snow - Season 1, Episode 2
Jon Snow was incredibly unhappy to be leaving Winterfell behind, especially after Bran's accident. He took on the wrath of Catelyn Stark one last time just to try and say goodbye to Bran. He wished with all his heart that he would wake up, and, of course, he did.
The fates of the two brothers are somehow interlinked so that Jon would indeed see Bran awake the next time that they crossed paths. Jon faced his worst enemies to be reunited with Bran; not every member of the Stark family could see the future with the same hopeful glance as Jon, who knew that the young heir would be ok.
"Look At You. You're A Man."
Jon Snow - Season 8, Episode 1
Jon Snow truly has missed years of Bran's life, since he's been trapped beyond the wall. One of his biggest regrets is leaving the Starks behind, considering what happened to the house when the War of the Five Kings began. Reuniting with Bran was a major moment that showed their bond.
Other people have looked down on Bran, horrifically suggesting he's less than a man because of the injury he has suffered. When Jon looks at the young Stark though, he sees someone who is just as wise and powerful as anyone else in the Stark household.
"Almost."
Bran Stark - Season 8, Episode 1
Bran Stark's response to Jon Snow is incredibly interesting. It's almost as if he can be truly honest with the Winterfell bastard, as both of them have felt out of place on some level or perhaps as if they don't fit in. Bran suggests that he's almost a man.
This is of course a reference to the mystical force that Bran has become. Jon might look at Bran strangely, but he quickly accepts it, considering the many things that he's seen beyond the wall; each just as impossible as the last. There's a level of true trust there.
"Father Is Watching."
Jon Snow - Season 1, Episode 1.
Even when Bran was younger, Jon Snow has looked out for him. Alongside Robb Stark, the brothers attempted to teach Bran how to fire an arrow. It was a poor effort from the young archer, who was never destined to be a strong warrior like other members of his family.
But within his advice, Jon mentions to Bran that their father, Ned is watching. It's a heads-up to Bran so that he can put his best foot forward to impress Ned. It shows that even though Jon wasn't the favorite, he wanted the other members of the family to be well-respected, especially Bran.
"He's the Son Of Rhaegar Targaryen."
Bran Stark - Season 7, Episode 7
Bran Stark sat on an incredibly important secret that could change the very fate of Westeros. He understood the significance of what he knew, that Jon Snow was actually the son of Rhaegar Targaryen and thus the true heir to the Iron Throne. But he only trusted this with Sam.
The fact that at this moment he went to Sam, essentially the brother of Jon Snow, shows how much respect he has for the bastard of Winterfell. He could have used the information to his advantage on any level but sought out advice from the one person that Jon respected the most.
"It's Your Choice."
Bran Stark - Season 8, Episode 4
Bran Stark completely appreciates where Jon Snow is in his life. The news that he's a Targaryen is groundbreaking and anyone else might have wanted to take control of such a powerful force; he is the future king after all. Bran doesn't do any of that though.
Instead, he offers Jon Snow a choice. Jon doesn't have those very often in his life. No matter what unpopular opinions there are out there about Jon, Bran clearly cares about doing right by Jon and thus demonstrates there are other paths forward, by trusting in him.
"So Our New King Has Chosen To Send You To The Night's Watch."
Tyrion Lannister - Season 8, Episode 6
Bran Stark had a very difficult decision to make. As the new king of Westeros he had to find a solution that would ensure everyone was happy. Specifically, he needed to find a way to remove Jon Snow from the situation, after killing Dany in the battle for King's Landing.
He managed to find the most merciful option available, sending Jon to the wall where he would be treated like a king. He had grown to love the north and while Tyrion might have delivered the news with some sadness, it was clearly the best option for Jon, showing how Bran will stick his neck out for him.
"There Are Five Pups. One For Each Of The Stark Children."
Jon Snow - Season 1, Episode 1
The Direwolves are the symbol of House Stark and represent the children of the powerful northern family. Jon Snow vouched for the Direwolf that the house found outside of Winterfell, suggesting that each pup should go to one of the children, including Bran.
While this was something that applied to the whole family, Jon would do a great service for Bran. He helped to forge the initial connection that would become so vital to the young man, who would actually be able to enter the mind of his wolf. That's impossible without his older brother's kindness.