In a small mixing bowl combine the egg and the 3 tablespoons milk. In a shallow bowl combine the crushed crackers, dried thyme, paprika, and pepper. Set aside.
Skin chicken, if desired. Dip chicken pieces, 1 at a time, in egg mixture, then roll in cracker mixture.
In a large skillet heat oil over medium heat. Add chicken and cook, uncovered, for 10 minutes, turning occasionally to brown evenly. Drain well.
Add the 1 cup milk to skillet. Reduce heat to medium-low; cover tightly. Cook for 35 minutes. Uncover; cook for 5 to 10 minutes more or until chicken is tender and no longer pink. Transfer chicken to a serving platter; cover and keep warm. Prepare Cream Gravy. If desired, serve with mashed potatoes and garnish with fresh thyme. Makes 6 servings.
Skim fat from drippings in skillet. Reserve 3 tablespoons of the drippings in skillet. In a screw-top jar combine milk, all-purpose flour, salt, and pepper; cover and shake until well mixed. Add to skillet. Stir in 1 cup additional milk. Cook and stir over medium heat until thickened and bubbly. Cook and stir 1 minute more. (If desired, thin with additional milk.) Makes about 1 1/2 cups gravy.