Prep the chicken: Pat thighs dry with paper towels.
Season both sides generously with salt, pepper, Italian seasoning, and smoked paprika if using.
Heat the pan: Set a large skillet over medium-high heat. Add 1 tablespoon olive oil and the butter. When hot and foamy, add the chicken, skin-side down if using skin-on.
Sear to build flavor: Cook without moving until deeply golden, 5–7 minutes.
Flip and cook another 3–5 minutes. Transfer chicken to a plate. It won’t be fully cooked yet; that’s okay.
Sauté aromatics: Lower heat to medium.
If the pan is dry, add another splash of oil (you can use the oil from the sun-dried tomatoes for extra flavor). Add garlic and red pepper flakes. Stir 30–45 seconds until fragrant.
Deglaze: Pour in the chicken broth and scrape up browned bits.
Let it simmer for 2 minutes to reduce slightly.
Build the sauce: Stir in the heavy cream, Parmesan, and sun-dried tomatoes. Simmer 2–3 minutes until the cheese melts and the sauce thickens enough to coat a spoon.
Return the chicken: Nestle the thighs back into the skillet and spoon sauce over the top. Reduce heat to medium-low and simmer 8–12 minutes, or until the internal temperature reaches 175°F for bone-in or 170°F for boneless.
Finish with freshness: Turn off the heat.
Stir in chopped basil and a squeeze of lemon juice if you like. Taste and adjust salt and pepper.
Serve: Spoon chicken and plenty of sauce over pasta, mashed potatoes, rice, polenta, or roasted vegetables. Garnish with extra basil and Parmesan.