4 large baking potatoes, scrubbed
2 tablespoons olive oil
salt, to taste
1 tablespoon butter
1 tablespoon flour
1 cup whole milk
½ cup sharp cheddar cheese
1 head broccoli, diced
Preheat the oven to 400 F. Use a fork to pierce the potatoes on all sides, then rub with olive oil and sprinkle with salt. Place on a rack set over a baking sheet, and bake 1 hour 30 minutes, turning every 30 minutes.
When the potatoes have been baking 1 hour, begin making the cheese sauce. Heat the butter and flour together in a saucepan set over low heat. Whisk together until a smooth paste forms, then drizzle in the milk. Whisk to combine, and bring to a simmer. When the sauce thickens, remove from the heat, add the cheese, and whisk to combine.
Place the diced broccoli in a bowl, cover with plastic wrap, and microwave on high for 1 minute. Remove the plastic, and stir the broccoli into the cheese sauce.
When the potatoes are fully cooked, split them and ladle the cheese and broccoli sauce on top.