Melt 6 Tbsp. butter in a 12-inch electric skillet. Brown chicken; set aside. Add mushrooms; brown to a golden color. Remove with slotted spoon and set aside. Add remaining 2 Tbsp. butter. Whisk in flour, salt, and pepper. Add chicken broth and milk; cook and stir until thick and bubbly. Place chicken and mushrooms in sauce. Cover; simmer 25 minutes on low.