Heat a cast iron skillet or Dutch oven with extra-virgin olive oil, a turn of the pan, over medium-high heat until very hot. Season the chicken breasts with salt and pepper, add to the pan and brown on both sides and cook through. Remove the chicken to a plate.
Add the salami to the pan and stir 1 minute, then add in the onions, celery, peppers, garlic and stir a couple of minutes more. Add the fennel seed and smoked paprika. Deglaze the pan with the red wine, then add the tomatoes, tomato sauce, parsley, and the reserved chicken. Bring the mixture to a boil and reduce to a simmer. Turn off the heat and cool completely to store for make-ahead meal.
Reheat in the same pan with a splash of water or stock to get things going. Top with an extra drizzle of extra-virgin olive oil and serve with bread crusted up in a hot oven.