Heat the oven to 425°F. Lightly oil a 9-by-13-inch baking dish or another 3-quart baking dish with a little of the olive oil.

Set a large deep skillet or Dutch oven over medium heat. Add 1 tablespoon of the olive oil.

Add the chopped onion and 1/2 teaspoon of the salt to the skillet. Cook for 5 to 6 minutes, stirring now and then, until the onion looks soft and lightly translucent.

Sprinkle the flour over the onion in the skillet. Stir for 1 minute so the flour coats the onion and loses its raw look.

Pour the milk into the skillet a little at a time, stirring well as you go so the sauce stays smooth. Pour in the vegetable broth and keep stirring.

Bring the sauce to a gentle simmer over medium heat. Cook for 2 to 3 minutes, stirring often, until it thickens enough to lightly coat the spoon.

Turn the heat to low. Stir the Dijon mustard into the skillet.

Add 6 ounces of the grated cheddar to the skillet, leaving the rest for the top. Stir until the cheese melts into the sauce.

Add the sour cream and black pepper to the skillet. Stir until the sauce looks smooth and creamy.

Add the drained cannellini beans to the skillet. Stir gently so the beans are coated with sauce.

Add the cooked brown rice to the skillet. Stir until the rice is evenly mixed into the sauce.

Add the chopped broccoli to the skillet. Fold it in until the broccoli is spread through the mixture, then taste and add the remaining 1/2 teaspoon salt if needed.