Locate or buy an electric fry-pan. Turn the unit on and raise the temperature to 350 degrees F. Pour in 1/4 to 1/2 cup peanut oil.
Dredge the chicken pieces in flour. Shake off most of the excess.
Arrange the chicken - skin-side down - in the pan. Cover with a lid. Watch the progress - closely. Peer under the chicken, periodically. Do not allow the chicken to become over-brown. Fry for 12-15 minutes on one side. Turn the chicken over, cover and fry for another 12-15 minutes.
Remove the chicken from the pan. Drain on paper towels. Season again with salt and cayenne pepper.
Pour off all but 2-3 Tbl of oil. Do not dislodge the brown bits on the bottom of the pan. Sift 1 1/2 Tbl of flour into the oil. Stir with a wooden spoon for a few minutes. Make a peanut butter in color roux. Break the roux down with 1 3/4 cups of whole milk. Stir and reduce. Adjust seasoning with salt and lots of black pepper. Reduce until the gravy is thick and bubbly. Serve the gravy on the side with the chicken.