Prep and season. Preheat the oven to 375°F (190°C).
Pat the chicken thighs very dry with paper towels. Season both sides with salt, pepper, and smoked paprika.
Brown the chicken. Heat a large oven-safe skillet or Dutch oven over medium-high heat. Add olive oil and 1 tablespoon butter.
Place the chicken skin-side down and sear until the skin is deep golden and crisp, about 6–8 minutes. Flip and sear the other side for 2–3 minutes. Transfer chicken to a plate (it will finish in the oven).
Build the flavor base. Reduce heat to medium.
Add remaining butter. Stir in garlic and red pepper flakes; cook 30 seconds until fragrant. Add the sun-dried tomatoes and stir for another minute.
Deglaze. Pour in the chicken broth, scraping up browned bits.
Simmer 2 minutes to reduce slightly.
Make it creamy. Stir in heavy cream, Parmesan, and Italian seasoning. Simmer gently 2–3 minutes until slightly thickened. Taste and adjust salt and pepper.
Add lemon juice if using for a little lift.
Add greens or mushrooms (optional). If using spinach, stir it in to wilt. If using mushrooms, sauté them in a separate pan first or add earlier with the garlic to release moisture.
Return chicken to the pan. Nestle the thighs into the sauce skin-side up. Spoon some sauce around (but not over) the skin to keep it crisp.
Sprinkle with chopped basil or parsley.
Bake. Transfer the skillet to the oven and bake 20–25 minutes, or until the chicken reaches 175–185°F in the thickest part for fall-off-the-bone tenderness. The sauce should be bubbling and rich.
Rest and serve. Let it rest 5 minutes. Garnish with more herbs.
Serve with mashed potatoes, rice, crusty bread, or buttered noodles to soak up the sauce.