Pat the chicken thighs dry with paper towels. Season generously on both sides with salt and pepper. Let them sit at room temperature for 15 minutes while you get your pan ready.
Brown the chicken: Heat your cast iron skillet over medium-high heat. Add 2 tablespoons of olive oil. When the oil is shimmering (not smoking), place the chicken thighs skin-side down. Do not crowd the pan — work in batches if you need to. Let them cook undisturbed for 6–7 minutes. The skin should be deep golden brown and release easily from the pan. Flip and cook for another 3 minutes. Transfer to a plate.
Brown the sausage: Add the sausages to the same pan. Cook for 4–5 minutes, turning occasionally, until they’re browned all over. Transfer to the plate with the chicken.
Sauté the peppers and aromatics: Reduce the heat to medium. Add the sliced bell peppers and cook for 4–5 minutes, scraping up the brown bits from the bottom of the pan. Add the smashed garlic, most of the sliced pepperoncini (save a few for the end), and the rosemary sprigs. Cook for 1 minute until fragrant.
Deglaze with wine: Pour in the white wine and let it simmer for 2 minutes, scraping up any remaining brown bits. The wine should reduce by about half.
Add stock and build the braise: Pour in the chicken stock. Nestle the chicken thighs and sausages back into the pan, skin-side up, tucking them into the peppers. Bring the liquid to a gentle simmer.
Braise in the oven: Transfer the skillet to a 375°F oven. Bake uncovered for 25 minutes.
The vinegar finish: Remove the skillet from the oven. Using tongs, transfer the chicken and sausages to a clean plate. Place the skillet back on the stovetop over medium heat. Add the white wine vinegar and the remaining sliced pepperoncini. Stir and let it simmer for 1 minute. Return the chicken and sausages to the pan, spoon the sauce over the top, and let everything rest for 5 minutes before serving.