Preheat oven to 400 degrees. Line a large rimmed baking sheet with foil, or parchment paper; set aside.
In a large bowl, stir together tomatoes, Hungarian or banana pepper, squash, mushrooms, olive oil, salt and black pepper until vegetables are coated with oil. Spread into a single layer on the prepared baking sheet. Bake 15 minutes, stirring once half-way through roasting. Remove from oven and drain excess liquids.
While vegetables roast, place sausage links in a large skillet over low-medium heat; tightly cover. Cook sausages about 15 minutes until cooked completely; turn sausages frequently. Remove cooked sausages to paper towel lined plate; blot excess grease.
In a small bowl, stir together mayonnaise, parmesan cheese and garlic; set aside.
Split and toast cut side of hoagie rolls. Spread an equal portion of the mayonnaise blend on the cut side of each roll. Cut sausage links in half lengthwise; place in roll to fill length of bread. Cut provolone cheese in half; place over sausage. Put sandwich under broiler for about 1 minute to melt cheese. Spoon an equal portion of the roasted vegetables over the top of sandwich. Enjoy!