Prep the chicken and vegetables: Pat the chicken thighs dry with paper towels and season both sides with 1 tsp kosher salt and 1/2 tsp freshly ground black pepper. Drying the meat helps get a proper sear — surface moisture turns to steam and prevents browning if you skip this step. Slice the onion, core and slice the peppers into 1/2" strips, mince the garlic, and dice the tomatoes.

Heat your skillet: Place a large (10–12") heavy skillet over medium-high heat and add 1 tbsp olive oil. When the oil shimmers (but before it smokes), add the chicken thighs in a single layer. Sear without moving for 3–4 minutes per side until a deep golden-brown crust forms. Searing develops the Maillard reaction — that brown fond on the pan creates concentrated flavor for the sauce.

Remove and rest the chicken: Transfer seared chicken to a plate and tent loosely with foil. Resting prevents the meat from drying during the sauce step; you'll finish cooking it in the sauce so slightly under-searing is fine.

Sweat the aromatics: Lower heat to medium, add remaining 1 tbsp olive oil and 1 tbsp butter to the skillet. When butter foams, add the sliced onion and a pinch of salt; sweat for 5–6 minutes until translucent and edges begin to caramelize. Add the peppers and continue cooking until peppers begin to soften, about 4 minutes. Cooking the onions and peppers slowly draws out sweetness and builds a flavor base for the cream.

Add garlic and flour: Stir in the minced garlic and cook 30 seconds until fragrant; then sprinkle 1 tbsp flour over the vegetables and stir for 30–45 seconds to cook the raw flour taste. Toasting the flour briefly helps it absorb liquid evenly and thickens the sauce without lumps.

Deglaze the pan: Pour in 1/2 cup chicken stock and scrape up the brown bits (fond) from the bottom with a wooden spoon. The fond dissolves into the liquid and becomes the backbone of your sauce — that's where much of the seared flavor goes.

Build the creamy tomato sauce: Add the diced tomatoes, 1 tsp dried oregano, 1/2 tsp smoked paprika, remaining 1/2 tsp salt and 1/2 tsp pepper. Simmer 4–5 minutes to reduce and concentrate flavors. Then stir in 1 cup heavy cream and bring to a gentle simmer. Reducing first intensifies the tomato flavor so the cream doesn't dilute it.

Finish the chicken in the sauce: Nestle the seared chicken thighs back into the pan, spoon sauce over them, reduce heat to medium-low, and simmer uncovered for 8–10 minutes until the internal temperature reaches 165°F (74°C). Cooking the chicken in the sauce finishes it gently and transfers moisture and flavor between protein and sauce.

Melt in the cheeses: Sprinkle the shredded mozzarella and grated Parmesan evenly over the chicken and sauce. Cover the skillet for 2–3 minutes to allow cheeses to melt. Then remove the lid and, if you want a lightly golden top, place the skillet under a hot broiler for 1–2 minutes — watch closely. Adding the cheeses at the end preserves their texture and gives the sauce a creamy, slightly stringy finish.

Rest and garnish: Remove from heat, let rest 3 minutes to thicken slightly, then finish with torn fresh basil and a drizzle of good olive oil if desired. Resting lets the sauce settle and makes serving cleaner and more flavorful.

Serve: Plate the chicken with a generous ladle of sauce and vegetables. It pairs beautifully with buttery mashed potatoes, creamy polenta, crusty bread, or a simple bed of pasta to soak up the sauce.