Pat the chicken dry with a paper towel and season on both sides with salt and pepper.
Heat oil in a large skillet or non-stick pan. Place the chicken top side down into the pan. Cook until deep golden brown.
Once the chicken skin is golden brown, flip the chicken and place in the oven.
Cook to an internal temperature of 160°F using a thermometer. Remove the chicken from the pan and set aside on a cutting board to rest.
Melt the butter in a saucepan on medium heat. Whisk in the flour and cook until it starts to turn golden brown. Whisk in the broth and bring to a simmer until the sauce reduces and thickens to a smooth consistency. Taste and add salt and pepper to taste. Stir in the cream until smooth.
Serve the sauce with the chicken and garnish with rosemary. Serve with dinner rolls.