Let's get the most obvious one out of the way: the trilogy's namesake ice cream. Cornettos almost have their own supporting role in these films as the go-to sweet for all of Wright's principals. Whether it's Nicholas and Danny snacking in their squad car, or Ed blithely eating a cone after he and Shaun kill their first zombies, Cornettos make up the literal dessert topping of the series.
The notion of the Cornetto trilogy came from a wisecrack Wright, Pegg, and Frost made following Hot Fuzz. With fans clamoring for a third film, the trio joked about the "ice cream connection" binding Fuzz together with Shaun, and later realized that both movies were alike in more ways than their characters' common fondness for frosty Cornetto deliciousness.