Heat olive oil in a large Dutch oven. Sprinkle turkey, duck, and chicken with salt and pepper and brown all pieces in the hot oil. Add the chicken broth, wine, water, peppercorns, thyme, and bay leaves, and bring to a boil. Reduce heat and simmer for 50 minutes.
Remove turkey, duck, and chicken, reserving stock. Remove and discard skin and bones. Cut meat into bite-size pieces and set aside 1 cup each of turkey, duck and chicken. Strain stock, skim off any fat, and set aside.
Melt butter in the Dutch oven. Add onion and potato and cook until lightly browned, about 5 minutes. Add carrots and celery and cook 2 minutes. Add flour; cook and stir for 3 minutes.
Stir in 5 cups stock and the 3 cups reserved meat; bring to a simmer. Cook until slightly thickened, about 3 minutes. Stir in parsley, peas, and TABASCO® Sauce. Transfer mixture to a 3-quart casserole dish or to ten 8-ounce ramekins.
Combine corn muffin mix with egg, milk, and sour cream. Stir until well combined and let sit for 5 minutes. Pour corn muffin mix on top of casserole and bake in a 400°F oven for 20 to 25 minutes.
Makes 10 (1-cup) servings.