Heat a cast-iron skillet or Dutch oven with EVOO, one turn of the pan, over medium-high heat until very hot. Season chicken breasts with salt and pepper, add to skillet and brown on both sides. Remove to a plate.
Add salami to the skillet and stir 1 minute. Add in the onions, celery, peppers, garlic and stir a couple of minutes more. Add fennel. Deglaze the pan with wine, then add the tomatoes, tomato sauce and parsley. Bring to a boil and then reduce to a simmer.
Return chicken breasts to the pot. Cook through, about 10-15 minutes, then turn off heat and cool to store for a make-ahead meal.