Chicken Divan Casserole

From The Kitchn - Grandma likes this - mostly I think because of the cream sherry ...

You can change up the cheeses - use cheddar or whatever you've got or change the veggies - add cooked mushrooms, cauliflower or whatever

4 boneless, skinless chicken breasts (approximately 2 pounds)
2 heads of broccoli (approximately 2 1/2 - 3 pounds)
4 tablespoons butter
5 tablespoons flour
2 cups warmed milk
1 cup grated Parmesan, divided
1 cup grated Gruyère/Swiss
3 tablespoons cream sherry
3/4 teaspoon salt
1/4 teaspoon black pepper

Add chicken breasts to a large pot. Add water to cover, season with salt and pepper. Bring to a boil, reduce heat to a simmer, and cover. Simmer until cooked through, and internal temperature has reached 160 °F. Remove chicken from pot, reserving broth. Cool and cut into 1/2-inch cubes or slices. (Feel free to use 4 cups of rotisserie or leftover chicken, if desired.)

Stem broccoli and cut into 1 – 2 inch florets. Bring chicken broth back to a boil and add broccoli (adding water if necessary). Reduce heat to medium-low and cook until broccoli is bright and tender, about 2 – 3 minutes - don't overcook. Strain broccoli and set aside.

Preheat oven to 375°F. Melt butter in a thick sauce pan on medium-low heat. Add flour and whisk until smooth (and flour taste is cooked out), about three minutes. Reduce heat to low. Pour in warmed milk and cook until thickened, approximately three to five minutes. Mix in 1/2 cup of Parmesan and one cup of Gruyère and stir until creamy. Add sherry, salt, and pepper. Remove from heat and set aside.

Butter the bottom and sides of an oblong casserole dish. Layer half of the broccoli and chicken and cover with half of the cheese sauce. Repeat. Sprinkle remaining Parmesan on casserole and bake until bubbly and golden brown, approximately 35 - 40 minutes. Serve with white rice.