Zucchini Rice Casserole

¾ cup long-grain brown rice
1 ½ cups chicken or vegetable broth
2 cups zucchini or summer squash, diced
1 red pepper, diced small
1 shallot, minced
½ teaspoon salt
white pepper
¾ cup cold milk
2 tablespoons all-purpose flour
2 cups shredded sharp cheddar cheese, divided
1 cup corn

1. Heat oven to 375°F and grease a 9-by-13-inch baking pan. Add rice to the pan. Bring broth to a simmer in a small saucepan. Stir hot broth into the rice along with zucchini, red pepper, onion and salt and white pepper. Cover with foil. Bake for 60-75 minutes until rice is tender and most of the liquid is absorbed.
2. Meanwhile, whisk milk and flour together in a small saucepan over medium heat. Cook until bubbling and thickened, 3 to 4 minutes. Reduce heat to low. Stir in 1 cup cheddar cheese and corn and cook, stirring, until the cheese is melted. Set aside. 
3. When the rice is done, remove the foil and stir in the cheese sauce. Sprinkle the remaining 1 cup cheese on top. Return the casserole to the oven and bake until the cheese is melted, about 10 minutes. Let stand for about 10 minutes before serving.