Preheat oven to 425º F.
With sharp kitchen shears (or carefully using a sharp knife), cut out the backbone of the chicken on each side of the spine. Cut off the wing tip sections (the outermost third portion of the wings) since they will tend to burn while roasting. Press the chicken with the bottom of a big skillet to flatten it out. Trim away any excess fat and skin.
Salt and pepper the chicken all over.
Heat the oil in a large (12”) cast iron skillet on the stove top until very hot. Add the butter and swirl until melted.
Lay the chicken into the hot pan, breast side down. Make sure the chicken is laying flat so it browns evenly on the legs and thighs.
Let the chicken sear for 5 to 7 minutes to develop a crust on the skin. A spatter screen is helpful here since the oil tends to pop out of the pan.
Using large kitchen tongs, carefully turn the chicken over to have the breast side up without breaking the skin.
Nestle the potatoes in around the chicken and scatter in the garlic cloves. Carefully turn the potatoes to coat them with oil - or use a small spoon to baste them along with the garlic.
Sprinkle a little salt and pepper around on the potatoes.
Using two pot holders and both hands, carefully place the skillet into the preheated oven.
Roast for 55 minutes to one hour. Use an instant read thermometer to make sure the chicken breast has reached at least 155ºF to 160ºF.
Again using two pot holders and both hands, carefully remove the skillet from the oven and let the chicken and potatoes rest for 20 minutes in the skillet before carving. During the resting period, the temperature of the bird will rise another 10 degrees.