Melt butter in heavy large Dutch oven over high heat. Add sausage, pepper, green onions, shallots, celery, garlic, thyme, sage, allspice, cayenne and bay leaves and sauté until vegetables are just tender and mixture is very moist, about 15 minutes. Stir vegetable mixture into corn bread. Season to taste with salt and pepper. (Can be prepared 1 day ahead. Cover and refrigerate.) Mix eggs into stuffing.