Toss the potatoes with paprika, thyme, salt, pepper, and half of the oil. Place them in an oven safe pan or foil lined baking sheet so they are not overlapping. Add the butter on top.
Drizzle the chicken with oil and massage in the seasoning rub.
Place the chicken skin-side up in an oven safe pan or foil lined baking sheet. Cook to an internal temperature of 160 degrees until the skin is golden brown and crispy. Then remove and set aside on a cutting board to rest before portioning. (Use the same pan as the potatoes if desired). If using an oven safe pan leave any drippings in the pan, if using a baking sheet pour any drippings into a saucepan.
After about 15 to 20 minutes flip the potatoes over.
Place the pan with the drippings on the stovetop over medium heat. Add in the broth if needed to add volume for the sauce. Bring to a simmer. Whisk in the cornstarch slurry a little at a time to thicken to a creamy consistency.
Remove the breast bones from the chicken and portion. Serve with potatoes. Spoon the sauce over the chicken and garnish with thyme sprigs. Serve with bread.