Heat broiler with rack set 4 inches from heat.
Cut broccoli into small florets; discard stalk.
Remove stems from mushrooms and discard. Slice mushrooms 1/2 inch thick.
Remove ribs and seeds from peppers and discard. Cut peppers into 1/2-inch thick slices.
Crush garlic through a press.
Thinly slice Gouda cheese (if not already sliced).
Line a rimmed baking sheet with aluminum foil.
Toss broccoli with oil, then season with 1/8 teaspoon salt and 1/8 teaspoon pepper. Add to baking sheet and broil 4-6 minutes, tossing once or twice until broccoli begins to char.
Add mushrooms and bell peppers to the broccoli; season with remaining salt and pepper and toss to combine. Broil 8-10 minutes more until vegetables are tender, stirring occasionally; set aside.
Meanwhile, combine mayonnaise and garlic in a small bowl.
Place bread on a work surface and cut into thin slices. Spread each slice with mayonnaise mixture; top with vegetables and then cheese. Place on baking sheet and broil 2-4 minutes until cheese is melted and lightly browned.
Slice melts in half for a snack or eat whole as a meal.