Where I come from we would call this a wedge, some people call it a hero, some call it a hoagie or grinder, so I am just going with Sausage and Peppers Sandwiches here and you can call them whatever you like.
Sausage and Peppers Sandwiches rank right up there with Grilled Chicken with Salmoriglio  as one of my standbys when I am getting my grill on in the summer. I remember once, years ago, I had a big cookout and my cousin Sal was working the grill. People would grab their roll, put it on a plate and walk over to the grill where Sal would load it up with sausage and peppers. Well, one of my co-workers (we called him Snowman) picked up his bread, slathered it with mustard and walked over to the grill. Sal was watching him the whole time like De Niro staring across the bar at Maury before he whacked him in Goodfellas. When he got to the grill, Sal calmly said “Snowman, don’t get me mad here. Go get a new roll.” And he was right, you just don’t put mustard on an Italian Sausage and Peppers Sandwich.
You can use sweet or hot Italian sausage, or both to satisfy everyone. Personally I like to put one sweet and one hot link in my sandwich. Best of both worlds! Some people get scared with sausage and are so afraid to undercook them, that they end up doing the opposite and drying them out. The best way to cook them on the grill is to start them out over the fire to get the outsides nice and browned then move them to indirect grilling to finish cooking gently. You will end up with perfectly cooked, juicy sausage.
There are a lot of choices for bread, you can cup up a long loaf of old school Italian bread, or use one of the fancier breads that are popular now. But if you ask me the perfect vehicle for grilled sausage smothered in sautéed peppers and onions is the humble club roll. It’s the perfect size and the texture is just right, substantial enough to handle the messy peppers and onions while still being easy to bite into. I used to get my club rolls from one of the good bakeries at Arthur Ave in the Bronx when I lived close by in Mt. Vernon. Now that I am in CT, too far to drive for just bread, I am lucky enough to have a local deli that gets their bread from those same bakeries.