Season carrots with brown sugar and celery salt in a bowl.
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add carrots, cover, and steam until tender, 2 to 6 minutes. Remove carrots and reserve hot water.
Melt butter in a large skillet over medium heat; cook and stir onion until slightly tender, about 3 minutes. Add mustard and flour to onion; cook and stir until flour is golden, about 5 minutes. Measure evaporated milk and enough reserved hot water to make 2 cups; stir into onion mixture. Continue to cook until sauce is smooth, stirring constantly, about 5 minutes. Season with pepper and more celery salt, if needed.
Layer half the carrots in a 2-quart baking dish. Arrange 2 slices Muenster cheese, 2 slices mozzarella cheese, and 2 slices provolone cheese over carrots and top with half the sauce. Repeat layers. Sprinkle bread crumbs over the final layer of sauce. Cover baking dish with aluminum foil.
Bake in the preheated oven until cheese is melted, 20 to 30 minutes.