Preheat oven to 350F. Move rack to middle position.
Season chicken with salt and pepper. Heat the oil in a large skillet.
When the oil is hot, add the chicken to the skillet skin-down. Cook for 8-10 minutes then flip it and cook it for an additional 4 minutes. Remove chicken from pan and set aside.
Deglaze the pan with the wine and mustard, stirring constantly until you've got a smooth sauce. Stir in the chicken broth, garlic, honey, Italian seasoning, butter, and salt & pepper to taste.
Add the chicken back in the pan and cook it in the oven for 45 minutes.