Pat dry and season. Pat the chicken thighs dry with paper towels. In a small bowl, mix all the Cajun seasoning ingredients. Sprinkle the thighs generously on both sides. Let them sit at room temperature for 15 minutes to take the chill off.

Preheat the pan. Heat a large oven-safe skillet (cast iron works best) over medium-high. Add olive oil and 2 tablespoons of butter.

Sear the chicken. When the butter is foamy and hot, place thighs skin-side down. Don’t crowd the pan; work in batches if needed. Sear 6–8 minutes until the skin is deep golden and crisp. Flip and sear the other side for 3–4 minutes. Transfer to a plate while you make the sauce base.

Brown the butter. Lower heat to medium. Add 3 tablespoons of butter to the skillet. Let it melt and cook until it smells nutty and you see browned bits forming, about 2–3 minutes. Scrape up the fond for flavor.

Build the sauce. Stir in the minced garlic and cook 30 seconds. Pour in the chicken broth and bring to a simmer, scraping the pan. Add a squeeze of lemon juice, a pinch of zest, and the remaining 1 tablespoon butter. If you like a hint of sweetness to balance the heat, add honey or brown sugar now.

Finish cooking. Return the chicken to the pan, skin-side up. Spoon some sauce over the meat, but keep the skin mostly uncovered so it stays crisp. Reduce heat to medium-low, cover loosely, and cook 8–12 minutes, or until the thickest part hits 165°F on an instant-read thermometer. Uncover for the last few minutes to re-crisp the skin.

Taste and adjust. Taste the sauce. Add more lemon, salt, or a splash of broth as needed. It should be silky, slightly tangy, and boldly spiced.

Garnish and serve. Sprinkle with chopped parsley. Serve with rice, mashed potatoes, grits, or roasted vegetables. Spoon extra Cajun butter sauce over everything.