Prep and season: Pat the chicken dry and season with 1 teaspoon salt and 1/2 teaspoon black pepper. Toss the potatoes with a pinch of salt and pepper.
Brown the potatoes: Heat 1 tablespoon olive oil in a large skillet or Dutch oven over medium-high heat.
Add potatoes cut side down and cook until golden, 6–8 minutes, turning occasionally. Transfer to a plate.
Sear the chicken: Add remaining 1 tablespoon olive oil. Sear chicken in two batches until lightly browned, 3–4 minutes per side.
Do not cook through. Transfer to the plate with potatoes.
Soften the vegetables: Reduce heat to medium. Add butter, onion, and bell peppers.
Sauté until softened and slightly caramelized, about 6–8 minutes. Stir in garlic for 30 seconds.
Deglaze with wine: Pour in white wine. Scrape up browned bits.
Simmer 2–3 minutes to reduce slightly.
Build the sauce: Stir in chicken broth, crushed tomatoes, oregano, thyme, and crushed red pepper (if using). Add cherry peppers and 2 tablespoons brine. Bring to a gentle simmer.
Combine and simmer: Return potatoes and chicken (plus any juices) to the pan.
Reduce to medium-low, cover partially, and simmer 12–15 minutes, stirring once or twice, until chicken is cooked through and potatoes are tender.
Adjust seasoning: Taste and add more salt, pepper, or cherry pepper brine for extra tang. If you want a thicker sauce, simmer uncovered for 3–5 more minutes.
Finish and serve: Sprinkle with fresh parsley. Serve hot with crusty bread, rice, or over pasta.
Add lemon wedges on the side for a fresh squeeze if you like.