In a large heavy-duty stockpot or Dutch oven over medium-high heat, add bacon, and lightly brown. Add oil and butter, and heat until butter is melted. Add meat, and brown evenly. While browning, season meat with salt and pepper. Stir in onion, carrots and celery, and cook until onions are translucent. Sprinkle flour over meat and vegetables while stirring. Cook for 5 minutes, stirring often.
Stir in beef or game stock, brandy, tomato paste and Italian seasoning. Bring to a boil, then reduce heat to low and simmer for 1½ to 2 hours or until meat is tender. If meat does not break apart with minimal finger pressure, keep cooking. If necessary, add additional stock to just below the top of the meat and vegetables. Add mushrooms and cook for 5 to 7 minutes more.
To prepare polenta, heat chicken broth and half-and-half to a boil in a large saucepan. Stir in butter. Stir in polenta or cornmeal, a little at a time. Continue to stir until mixture is hot and bubbly. Reduce heat to low, and cook for 20 to 25 minutes, stirring frequently. Stir in cheese, and season to taste with salt.
To serve, spoon polenta into large bowls and spoon ragout over.