Season the chicken: Pat chicken dry. Season generously with salt and pepper on both sides. This helps the skin crisp and flavors the sauce later.
Brown the chicken: Heat 2 tablespoons olive oil in a large, heavy skillet or Dutch oven over medium-high heat.
Sear chicken skin-side down until golden brown, about 5 to 7 minutes. Flip and sear the other side for 3 to 4 minutes. Transfer to a plate.
Don’t cook through yet.
Sauté the vegetables: Pour off excess fat if needed, leaving about 2 tablespoons in the pan. Add onions and peppers with a pinch of salt. Cook over medium heat until softened and lightly browned, about 6 to 8 minutes.
Stir in mushrooms and cook until they release moisture and start to brown, about 5 minutes.
Add aromatics: Stir in garlic and red pepper flakes. Cook 30 seconds, just until fragrant. Add tomato paste and cook 1 minute to caramelize slightly.
Deglaze with wine: Pour in red wine and scrape up browned bits from the bottom of the pan.
Simmer 1 to 2 minutes to reduce slightly. If not using wine, use a splash of broth and a teaspoon of red wine vinegar for brightness.
Build the sauce: Add crushed tomatoes, capers, olives (if using), oregano, bay leaf, and a few thyme sprigs if you have them. Stir to combine.
If the sauce seems very thick, add 1/2 cup broth to loosen.
Nestle in the chicken: Return chicken and any juices to the pan, skin-side up. The chicken should be mostly submerged, with the skin peeking out. Reduce heat to a gentle simmer.
Simmer until tender: Cover partially and cook 25 to 35 minutes, until chicken is cooked through and tender.
Thighs should reach 175°F internally for best texture. Stir occasionally to prevent sticking.
Adjust and finish: Remove bay leaf and herb stems. Taste the sauce.
Add salt, pepper, or a pinch of sugar if the tomatoes are very acidic. If you want a silkier sauce, stir in a small knob of butter at the end. Sprinkle with chopped parsley.
Serve: Spoon chicken and sauce over al dente pasta, creamy polenta, or mashed potatoes.
Finish with a drizzle of olive oil and a little grated Parmesan if you like.