For the sage brown butter add the sage and stick of butter to a pot over medium-low heat. Melt the butter and stir every so often until the milk solids begin to caramelize and a simmering begins. Once the butter turns a golden amber color and smells nutty and toasty (which happened very quickly). Pull the butter from the stove, remove the sage leaves, and add it to another bowl sitting over a big bowl of ice water. Whisk the butter until it rehardes and turns to a whipped smooth butter consistency.
For the chicken, pat it dry with paper towels and season generously with salt, inside and out then let the chicken sit at room temperature for an hour.
Preheat oven to 425° and place your cast iron skillet in the middle to preheat as well.
In a bowl add the sliced sweet potatoes, 1 tablespoon of melted sage brown butter, the chopped sage and thyme, a big pinch of salt and oil then toss.
Once the oven is ready, pat the chicken dry again, take 2 tablespoons of the softened sage butter, and rub it all over the exterior of the chicken. Carefully remove the skillet from the oven and place the chicken in the center and the sliced potatoes all around the chicken.
Roast for about an hour or until the potatoes are roasted golden brown and the chicken s firm to the touch. (You can check the thickest part of the breasts with a thermometer for 155° as the temperature will climb to 165° as the chicken rests). Let chicken rest in skillet for at least 20 minutes and up to 45 minutes.
Transfer the chicken to a cutting board and carve. Serve with potatoes.