Prep the chicken: pat the chicken breasts dry with paper towels and season both sides generously with 3/4 tsp kosher salt and 1/4 tsp black pepper. Drying the surface removes moisture so the chicken will sear (not steam) and develop a flavorful golden crust.

Slice the vegetables: thinly slice the onion and bell peppers, mince the garlic, and dice the tomatoes. Keeping slices uniform ensures even cooking and a balanced texture throughout the dish.

Warm a 12-inch (30 cm) heavy skillet over medium-high heat and add 1 tbsp olive oil. When the oil shimmers, add the chicken breasts (do not crowd the pan). Sear 3–4 minutes per side until a deep golden-brown crust forms and the internal temperature reads ~62–64°C (145–147°F). Searing creates the Maillard crust that deepens flavor — we’ll finish cooking the chicken in the sauce so slightly undercooking is fine.

Transfer the chicken to a plate and tent loosely with foil. Reduce heat to medium, add the remaining 1 tbsp olive oil and 2 tbsp butter to the same skillet. Leaving the fond (brown bits) in the pan adds concentrated flavor to the sauce — don’t scrape them away yet.

Add the sliced onions and peppers to the skillet. Season with a pinch of salt and sauté 6–8 minutes until the onions are translucent and the peppers begin to soften and caramelize. Sweating and caramelizing concentrates sweetness and builds complexity in the base of the sauce.

Stir in the minced garlic, smoked paprika, dried oregano and red pepper flakes; cook 30–45 seconds until fragrant. Toasting the spices briefly in fat blooms their essential oils and intensifies aroma — be careful not to burn the garlic.

Deglaze the pan with 120 ml (1/2 cup) chicken broth, using a wooden spoon to scrape up the fond. Deglazing lifts those caramelized bits into the liquid, creating a deeply flavored base for the cream sauce.

Add the diced tomatoes and simmer 3–4 minutes to soften them and concentrate their flavor. The tomatoes introduce acidity that brightens the richness of the cream and cheese.

Reduce heat to low and stir in 240 ml (1 cup) heavy cream. Heat gently until the cream is warm but not boiling (boiling can cause cream to separate). If you prefer a slightly thicker sauce, dissolve 1 tsp cornstarch in 1 tbsp cold water and whisk it in now — the small amount of starch stabilizes and thickens without clouding the sauce.

Stir in the shredded cheddar and mozzarella a handful at a time until melted and smooth. Keep the heat low and stir continuously — adding cheese slowly prevents clumping and ensures a silky emulsion.

Return the seared chicken breasts to the skillet, nestling them into the sauce. Spoon sauce over the chicken, cover, and simmer on low for 6–8 minutes, or until the chicken reaches 74°C (165°F) internal temperature. Finishing the chicken in the sauce keeps it moist and lets flavors meld.

Taste and adjust seasoning with the remaining 1/4 tsp salt and 1/4 tsp black pepper if needed. Turn off the heat and scatter chopped basil or parsley over the dish for freshness and color. Let the skillet rest 2 minutes — the sauce will thicken slightly as it cools.

Serve: Spoon the creamy peppers, onions and tomatoes over the chicken and finish with an extra pinch of smoked paprika or red pepper flakes if you like heat. Serve with a simple green salad, crusty bread, or over buttered pasta, rice or cauliflower rice for a lower-carb option.