Toss asparagus and red pepper with olive oil. Place on a lined baking sheet and bake until tender, about 10 minutes. Once cool enough to handle, remove skin from the pepper and slice into strips.
Cut hoagie rolls in half, place on a baking sheet, and toast lightly in the oven. Remove rolls from the oven and sprinkle each half with cheese. Place 4 to 5 asparagus spears and a few strips of pepper on one side. Place slices of tomato on the other side of the roll. Place the hoagies back in the oven until the cheese is melted, about 5 minutes.
Meanwhile, in a separate bowl, mix the mayonnaise, lemon juice, and garlic together. Spread the dressing on one side of the roll and close sandwich.
