Pat the chicken thighs dry with paper towels and season generously with salt and pepper.
Heat the olive oil in a large skillet or Dutch oven over medium-high heat. Brown the chicken on both sides, working in batches so the skin gets crisp, about 4–5 minutes per side. Transfer to a plate and set aside.
Reduce heat to medium. In the same pot, add the onion and a pinch of salt. Sauté until the onion becomes translucent and just beginning to brown, about 4–5 minutes.
Add the garlic and peppers. Cook for 2–3 minutes, until the garlic is fragrant and the peppers have softened a bit.
If using mushrooms, add them now and cook until they release their moisture and start to brown, about 4 minutes.
Pour in the white wine (or stock) to deglaze the pan, scraping up any browned bits from the bottom. Let the liquid reduce by about half, 2–3 minutes.
Return the chicken to the pot. Add the crushed tomatoes, oregano, basil, and red pepper flakes. Stir gently to combine.
Bring to a gentle simmer. Reduce the heat to low, cover, and cook for 25–30 minutes, or until the chicken is tender and the flavors have melded.
Stir in olives and capers, if using, and simmer uncovered for 5–8 minutes to blend the flavors. Taste and adjust salt and pepper as needed.
Garnish with chopped parsley and serve hot. This pairs beautifully with crusty bread, polenta, or spaghetti.