Preheat oven to 400 degrees F.
Season the chicken liberally with salt and pepper, poultry seasoning, and grill seasoning. Heat 2 tablespoons olive oil in a medium skillet and brown the chicken a few minutes on each side to put some of it's flavor and drippings into the pan then transfer to oven and roast 15 minutes more or until juices run clear. Meanwhile, add 1 more tablespoon olive oil to the pan and cook pancetta or bacon, if using, until crisp. Add onions, garlic and rosemary, cook 5 minutes then add the vinegar, sugar, Worcestershire, tomato sauce and 1/2 cup chicken stock, reduce heat to low and let sauce simmer 5 minutes more.
Bring remaining 1 1/2 cups stock and milk to a boil, whisk in polenta and season with salt and pepper. Whisk polenta 2 to 3 minutes until it thickens, stir in butter and cheese, remove from heat.
Remove chicken from oven and turn in barbecue sauce. Fill shallow bowls with polenta Top with chicken, spoon extra sauce over chicken and garnish with some torn basil leaves.