Preheat the oven to 400°F. Lightly coat an 8 by 8-inch baking pan with nonstick cooking spray.
Cook the macaroni according to the package directions until al dente (just firm). Add the carrots 3 to 4 minutes before the pasta is finished. Using a slotted spoon, skim off any foam that rises to the surface. Drain and set aside.
Meanwhile, in a saucepan over medium heat, melt 3 tablespoons of butter. Whisk in the flour until it’s completely incorporated, about 1 minute, whisking constantly. Add the milk and cook until thickened, whisking constantly. Reduce the heat and cook for 3 to 5 minutes, whisking often.
Remove from the heat and add the cheddar cheese, salt, mustard, and pepper. Stir until the cheese has melted. Add the pasta mixture and stir well to combine. Transfer to the baking pan.
Melt the remaining tablespoon of butter. In a small bowl, mix the bread crumbs with the melted butter. Stir in the Parmesan. Sprinkle on top of the macaroni mixture. Bake for 15 to 20 minutes, until the top is golden brown. Remove from the oven and let cool just slightly before serving.