The wedge is the Westchester County word for the long-roll sandwich, and the word is the most interesting thing about it. In a stretch of suburban New York just north of the city, the same sandwich the next county calls a hero, the city calls a hero, Philadelphia calls a hoagie, and New England calls a grinder is called a wedge, and locals will correct you on it. The term is a dialect marker, a small linguistic border drawn around a few towns, and ordering a wedge instead of a hero is one of the quiet ways the area signals where it is from. The sandwich underneath the name is the long-roll sandwich; the name is the regional fact worth knowing.
The build follows the same founding principle every name in this family runs on: a long roll, split, layered the full length so every bite holds the whole sandwich, with the roll chosen as a structural component rather than a wrapper. The Westchester wedge typically uses a length of Italian bread with a real crust, sturdy enough to carry a heavy, often dressed load without folding in the middle and tender enough inside not to fight the filling. The cold Italian build shingles cured meats and provolone so each bite gets all of them, then uses oil, vinegar, and shredded lettuce as a system that seasons and lubricates without dissolving the bread; the hot builds turn the roll into a vessel for a saucy filling and lean on a quick toast to keep it intact.
The variations are the same architecture under different fillings: the Italian combination, the chicken or eggplant parm, the meatball, the tuna, and the turkey, each a codified build with its own rules. Why one cluster of New York towns settled on wedge while the county beside it kept hero is a question of regional speech rather than of bread engineering, and the parallel naming traditions, the hero and the hoagie and the grinder, each deserve their own article rather than being crowded in here.