Preheat the oven to 400°F (200°C) and place a rack in the middle.

Pat the chicken thighs very dry with paper towels. Season both sides with kosher salt and freshly ground black pepper.

Heat an oven-safe skillet over medium-high heat. Add 2 tablespoons of butter and 2 tablespoons of olive oil until the fat shimmers.

Place the thighs skin-side down and press gently. Sear until deeply golden, about 6 to 8 minutes. Flip and sear the meat side for 1 to 2 minutes, then transfer to a plate.

Lower heat to medium. Add remaining 2 tablespoons of butter to the pan. When melted, stir in garlic, paprika, Italian seasoning, and red pepper flakes. Sauté about 30 seconds; do not let garlic burn.

Add grated Parmesan and stir until slightly melted and combined with the butter.

Return thighs skin-side up to the skillet. Spoon sauce over the meat and around the thighs. Transfer skillet to the oven.

Bake for 15 to 20 minutes until an instant-read thermometer reads 165°F (74°C). Broil 1 to 2 minutes for browning if desired.

Remove from oven and let thighs rest for 5 minutes. Sprinkle with chopped parsley before serving.