Heat broiler, with rack set 4 inches from heat. On a rimmed baking sheet lined with aluminum foil, toss broccoli with oil; season with salt and pepper. Broil, tossing once or twice, until broccoli begins to char, 4 to 6 minutes.
Add mushrooms and bell peppers to sheet; season with salt and pepper, and toss to combine. Broil, tossing once or twice, until vegetables are tender, 8 to 10 minutes more; set aside.
Meanwhile, in a small bowl, combine mayonnaise and garlic; season with salt and pepper. Place bread on a work surface. Dividing evenly, spread with mayonnaise mixture, and top with vegetables, then cheese. Place on baking sheet, and broil until cheese is melted and lightly browned, 2 to 4 minutes.