Gently wash produce under cool running water, pat dry, and prepare as directed.
Preheat the oven to 350°F.
Prick the potato skins with a fork in several places and wrap with aluminum foil.
Bake the wrapped potatoes 30-60 minutes, until soft inside. Check doneness by piercing with a fork.
Place the broccoli, onion, and carrots in a microwave-safe dish with 2 Tbsp water. Cover and microwave until tender, about 5 minutes. Drain and set aside.
Melt the butter in a saucepan. Stir in the flour. Slowly add the milk while stirring continuously, and cook a few minutes until the sauce thickens.
Add the shredded cheese to the sauce and stir until melted. Add the cooked vegetables to the cheese sauce. Season with salt and pepper to taste.
Unwrap the potatoes and place on a serving plate. Slice the top of each potato lengthwise and spoon the sauce into the opening.