Season chicken with salt and pepper. Heat olive oil in a large skillet over medium-high heat and brown chicken 4–5 minutes per side until golden; transfer to a plate.
Add sliced onion to the same pan and cook 3–4 minutes until translucent.
Stir in minced garlic, sliced bell peppers and mushrooms; sauté 4–5 minutes until softened.
Pour in white wine to deglaze the pan, scraping up browned bits; cook 1–2 minutes to reduce (or use extra broth if avoiding alcohol).
Add crushed tomatoes, tomato paste, oregano, thyme, bay leaf and chicken broth; stir to combine.
Return browned chicken to the pan, nestling pieces into the sauce so they are partially submerged.
Bring to a gentle simmer, cover and cook 25–30 minutes until chicken reaches 75°C (165°F) and is tender.
Remove lid and simmer 5–10 minutes more to thicken the sauce to your liking.
Stir in capers or olives if using; taste and adjust seasoning with salt, pepper and a pinch of red pepper flakes.
Garnish with chopped fresh parsley and serve hot over pasta, polenta or with crusty bread.