Dredge duck pieces with seasoned flour. Heat grease or oil in a large skillet over medium-high heat. When oil is hot, add breasts, skin side down and cook until skin is crisp, about 3 to 5 minutes. Flip breasts over and add garlic and onion. Cook for 3 minutes. Transfer everything to a roasting pan. Add wine one cup of the of chicken broth, celery and carrot. Cover with lid or foil and place in a 375 degree preheated oven. Add additional wine or stock if liquid evaporates. Duck will be very firm before it gets to the tender stage. Test for doneness after about 1 hour and continue cooking as needed.

In a saucepan, heat remaining chicken broth with mushrooms and cook untl mushrooms soften. Add basil and tomato and heat to warm. Remove from heat and whisk in butter pieces until melted. Season with salt and pepper. Serve cooked duck over polenta and top with cheese before serving.