Pat chicken dry with paper towels. Season with half the salt and the pepper. Heat 1 tablespoon oil in a wide Dutch oven over medium-high heat. Brown half the thighs for 3–4 minutes per side, then transfer to a plate. Repeat with remaining oil and chicken; it will finish cooking in the sauce.

Add onion, pepper and mushrooms to the pot. Cook 8–10 minutes, stirring, until softened and mushroom moisture mostly evaporates. Stir in garlic and oregano for 30 seconds.

Add tomatoes with juices, broth and remaining salt. Scrape up browned bits. Return chicken and accumulated juices, bring to a simmer, then reduce heat and partly cover. Simmer gently 20–25 minutes, checking each thigh for at least 165°F in its thickest part. Continue if needed.

If sauce is too thin, transfer fully cooked chicken to a clean plate and simmer sauce uncovered for a few minutes; return chicken briefly to heat through. Divide chicken and sauce into six servings. Refrigerate leftovers promptly in shallow containers within 2 hours (1 hour above 90°F), keep at 40°F or below, use within 3–4 days and reheat throughout to 165°F.