Place a cast-iron skillet over medium-high heat. Add 1 tablespoon butter and oil to skillet. Heat until butter is melted.
Pat chicken thighs dry with paper towels and season all over with salt and pepper.
Sear chicken in hot skillet until golden brown on both sides, about 5 minutes per side. (I start with the skin side down so it finishes facing up.)
Remove chicken from skillet and place on a baking sheet, skin side up. Keep warm in the oven while you prepare the sauce. (see note)
To the skillet 4 tablespoons butter, honey, vinegar, and garlic. Whisk and bring sauce to a simmer. Cook for 2-3 minutes until the sauce beings to thicken. Add chicken back to the skillet. Continue cooking until sauce thickens, about 4 to 5 minutes.
Spoon sauce over chicken and garnish with chopped parsley. Serve warm.
You can also use bone-out, no skin thighs, or 4 chicken breasts for this recipe. For boneless thighs, you don’t need to cover and cook longer like the bone-in variety. For breasts, cook for 5-6 minutes per side before moving on to the sauce. As long as your chicken is 165 degrees F internally, you’re good to go.
I like to finish these thighs in the oven since I usually have preheated to roast some potatoes and broccoli to go with our meal. (They take just as long as the chicken so everything finishes together.) If you want to skip the oven, reduce stove heat to medium, and cover the skillet. Cook chicken for another 5 minutes, until cooked through. Then remove the chicken to a plate or baking sheet while you start the sauce.