Season chicken thighs with salt, pepper and cayenne pepper.
Place butter and olive oil in a skillet over medium heat. Once butter is melted and hot, add the chicken and sear on each side until well-browned, about 3-4 minutes per side.
In a small bowl, whisk together the mustards, honey and garlic until completely combined.
Divide the honey-mustard mixture over each chicken thigh and place skillet in the oven.
Bake for 18-20 minutes until chicken reaches an internal temperature of 165F.