Preheat oven to 350 degrees F (175 degrees C). Grease the inside of a 2-quart casserole dish.
Boil carrots in a pot of lightly salted water until slightly tender, about 10 minutes. Add zucchini and onion; boil until zucchini is tender, 5 to 10 more minutes. Drain.
Melt 2 tablespoons butter in a large skillet over medium heat. Whisk flour into melted butter forming a paste, 1 to 2 minutes. Stir half-and-half into paste, stirring constantly, until mixed. Add bouillon cubes and stir until dissolved, 1 to 2 minutes. Add Colby-Jack cheese, mustard, and dill; whisk until cheese is melted, 2 to 3 minutes. Stir in vegetables. Transfer mixture to prepared casserole dish.
Mix bread crumbs with 1/4 cup melted butter in a bowl until butter is fully incorporated. Sprinkle over top of casserole.
Bake casserole in the preheated oven until bubbling and topping is browned, about 45 minutes.
