Preheat oven to 300 degrees F.
Heat a Dutch oven over high heat with the 2 tablespoons olive oil. Saute the onion, celery, carrots and fennel in a Dutch oven, with the salt and paprika, until soft. Remove to a small bowl.
In another tablespoon of olive oil, saute the chicken breast pieces over high heat, turning to brown on both sides. Remove the chicken to a plate.
Heat the dutch oven back up with a tablespoon of butter. Brown the mushroom slices, turning to brown both sides. Remove the mushrooms to a bowl.
De-glaze the pot with the wine, stirring to get the particles off the bottom of the pan. Add the chicken broth in, continuing to simmer. Add the chicken back in to the Dutch oven, then the potatoes, soffrito (onion, celery, fennel and carrots), mushrooms, thyme and Herbs de Provence. Cover and place in the center of the oven. Cook for one hour, 20 minutes to an hour and a half. Ladle into bowls and top with parsley (or oregano) if you don't have parsley on hand! Serve with crusty French bread.