Season chicken with salt and pepper.
Heat Dutch oven over medium heat, add 1 tablespoon of olive oil, add sliced sausage, stirring till browned about 2 minutes.Transfer sausage to a plate.
Raise heat to medium, add the chicken to brown both sides, 4-6 minutes per batch and also set aside.
Add remaining 1 tablespoon of olive oil to the pot. Add cauliflower, red pepper, onion,and garlic and cook for about 5 minutes until onions are translucent. Add the artichokes, hot cherry peppers, and white wine to the pan.
Let wine reduced to about half, add back in chicken and sausage and the sprig of rosemary.
Add in the chicken broth. Bring to a boil, lower heat, cover, simmer till chicken cooked through, about 25 minutes,
Use a slotted spoon, transfer chicken and veggies to a large bowl. Bring liquid to a boil, let boil to reduce to about two thirds and thicken, about 15 minutes. Pour sauce over chicken and serve.