Pat the chicken thighs bone-dry with paper towels (moisture is the enemy of a good sear). Season both sides generously with salt and pepper. Place the ½ cup of flour in a shallow bowl and lightly dredge each thigh, shaking off the absolute excess.Why: This creates the crust and provides the starch needed to thicken the sauce later. Heat 3 tbsp of olive oil in your 12-inch heavy skillet over medium-high heat until shimmering. Place chicken thighs skin-side down. Use your splatter guard. Sear for 6–8 minutes without moving them until the skin is deep golden and releases easily from the pan. Flip and sear for 2 minutes on the other side. Remove to a platter (they won't be fully cooked yet).
In the same pan, add the whole sausage links. Brown them for 3–4 minutes per side. Once browned, move them to the cutting board, slice into 1-inch rounds, and return them to the pan for 1 minute to crisp the edges.Note: If the pan is too dry, add one more splash of oil. If there is more than 3 tbsp of fat, spoon some out. Transfer the chicken to a plate. Keep it uncovered so the steam doesn't soften the skin you just crisped.
Add the sausage links to the chicken fat. Brown them whole first, then remove, slice into rounds, and toss them back in for 1 minute to crisp the edges.
Add the smashed garlic and fresh rosemary sprigs. Sauté for 1 minute until fragrant.
Add the sliced bell peppers and the jarred hot cherry peppers. Sauté for 3–5 minutes until the bell peppers soften.
Pour in the white wine. Use a flat spatula to scrape up all the brown bits (the "fond") from the bottom of the pan. Let the liquid reduce by half.
Add the chicken broth, 2 tbsp pepper brine (vinegar), and dried oregano. Bring to a simmer.
Nestle the chicken back into the pan on top of the peppers. Do not submerge the skin. Simmer for 12–15 minutes until the internal temperature is 165°F.
Turn the heat to high for 2 minutes, then turn it off and whisk in 2 tbsp cold butter and the lemon juice/zest.
Spoon the sauce and peppers around the chicken. Garnish with fresh parsley for a pop of color and freshness.