Prep the chicken: Pat the chicken dry.
Season both sides with salt, black pepper, and half the dried oregano. If the breasts are thick, pound them to an even thickness for faster, even cooking.
Heat the pan: Set a large skillet over medium-high heat. Add 2 tablespoons olive oil.
When it shimmers, add the chicken in a single layer.
Sear the chicken: Cook 4–5 minutes per side until browned and almost cooked through. Remove to a plate. Don’t wipe the pan; those browned bits equal flavor.
Sauté aromatics: Lower heat to medium.
Add a splash more oil if needed, then the chopped onion. Cook 3 minutes until softened. Add garlic and red pepper flakes, and cook 30 seconds until fragrant.
Build the sauce: Stir in the canned tomatoes, cherry tomatoes (if using), remaining oregano, and chicken broth or white wine.
Scrape up browned bits from the pan. Simmer 5–7 minutes to thicken slightly.
Return the chicken: Nestle the chicken back into the sauce. Simmer 4–6 minutes, or until the chicken reaches 165°F and the sauce tastes concentrated and bright.
Finish with freshness: Stir in butter (if using) for silkiness.
Add balsamic vinegar or lemon juice to sharpen flavors. Fold in most of the basil, saving a little for garnish. Taste and adjust salt and pepper.
Serve: Spoon the sauce over the chicken.
Top with remaining basil, a sprinkle of Parmesan if you like, and optional capers or sliced olives. Pair with pasta, couscous, rice, or bread.