Pat the chicken thighs dry and season both sides generously with salt and black pepper. Keeping the skin dry helps it brown properly during searing.
Heat the olive oil in a large skillet over medium-high heat. Place the chicken skin-side down and cook for 4–5 minutes per side, until deeply golden. Transfer to a plate, then brown the sausage pieces in the same skillet for 3–4 minutes. Set them aside with the chicken.
Reduce the heat to medium and add the onion and red bell pepper to the skillet. Cook for 4–5 minutes until softened and lightly caramelized. Stir in the garlic and cherry peppers and cook for another minute.
Pour in the white wine and reserved cherry-pepper brine, scraping up the browned bits from the bottom of the skillet. Simmer for 3-4 minutes, allowing the liquid to reduce slightly.
Return the chicken and sausage to the skillet. Add the chicken broth, lemon juice, and rosemary. Cover and simmer gently for 15-20 minutes, or until the chicken reaches at least 165°F in the thickest part.
Transfer the chicken and sausage to a serving platter if desired. Whisk the butter into the hot pan sauce until glossy, then stir in the fresh parsley and a final squeeze of lemon juice.
Spoon the peppers, onions, sausage, and pan sauce over the chicken. Serve immediately with crusty bread, roasted potatoes, or pasta to soak up the tangy, buttery sauce.