Slowly pour the chicken broth into the skillet and stir to fully dissolve the flour from the bottom of the skillet. The flour will start to thicken the sauce when it returns to a simmer. Add black pepper, Italian seasoning, 1/2 cup cheddar cheese, 1/2 cup mozzarella cheese, and the nonfat milk to the skillet. Stir until the cheese is melted and the sauce is smooth.