Cook butter and flour together in sauce pan till bubbly.
Add milk and chicken broth and stir until smooth and begins to bubble again.
Chop broccoli, carrots, and onion. Add to the sauce and stir to coat all veggies. Pour into a prepared pie crust. Top with cheese. *Optional: If you have any leftover cooked chicken, top the veggies with your chicken. Sometimes, I'll do a half and half pie- half with chicken, half without.
Top with shredded cheddar cheese, and then another pie crust for the top.
Bake at 400 degrees for about 40 minutes, or until your pie crust is browned and cooked.