Rinse and dry the skillet used for the chicken, and heat it over medium heat. Melt butter in the hot skillet, and whisk in flour. Very slowly stir in milk a tiny bit at a time, whisking constantly until smooth before adding more. When all the milk is incorporated, continue whisking often and bring to a simmer until thick and bubbly. Turn heat to low, and stir in parmesan, pepper, and salt. Turn off heat, and evenly spread white sauce over the dough.