Season the bird inside and outside with salt and pepper. Tie the legs of the chicken tightly together with kitchen string. (Truss the entire bird - if desired.)
In the microwave, soften the butter. Smear it over the entire surface of the chicken.
Once the oven preheats to 400 F, place the bird on one of its "lateral sides" (on a leg and wing side) in the preheated pan. Roast for 15 minutes. Turn the chicken to the other "lateral side". Roast for 15 more minutes.
Turn and place the chicken back-side down in the pan. Baste it - lavishly - with the juices and the fats of the pan. Roast for 25-35 minutes. From time to time, baste the bird. Test for doneness (with a temperature probe) after 25 minutes.
Remove the pan from the oven. Place the chicken on a platter. Degrease the pan. Melt 3 Tbl butter in the pan. Sprinkle in 2 Tbl of flour. With a small whisk, make a peanut butter colored roux. Break down the roux with 2 cups of whole milk. Scrape the bottom of the pan to liberate the brown bits. Pour in 2 oz of heavy cream. Reduce the gravy until it is thick and bubbly. Adjust seasoning with a little salt, cayenne pepper and lots of black pepper.
Hack the chicken into quarters. Serve with rice or biscuits. Ladle the sawmill gravy - copiously - over both.