Preheat the oven to 425 degrees F.
In a small bowl, combine the kosher salt and pepper.
Lay the potatoes close together in one layer on a sheet pan. Drizzle the potatoes with 1 tablespoon olive oil and season with 1 teaspoon kosher salt and pepper mixture and add 4 sprigs of thyme. Gently toss the potatoes.
Remove the wings from the chicken. Loosely stuff the chicken cavity with 1 teaspoon salt and pepper mixture, lemon, garlic and 2 sprigs of thyme.
Push about 4 tablespoons butter underneath the chicken skin. Season the outside of the chicken and the wings with remaining salt and pepper. Place the chicken wings on the edge of the potatoes and dot them and the potatoes with the remaining butter.
Place the chicken on its side on top of the potatoes. Put it in the oven for 20 minutes.
Turn the chicken over onto its other side and flip the wings over, roast for another 20 minutes.
Take out the wings. Turn the chicken onto its back, to roast it breast-side up for another 10-20 minutes. Add ¼ cup of water to the potatoes if necessary.
Once chicken is done, let rest for 5-10 minutes. Carve the chicken in the pan so that the juices can run into the potatoes some more and serve.