Meanwhile, bring broth to a boil in a Dutch oven; slowly stir in grits. Cover, reduce heat, and simmer 5 minutes or until done. Remove from heat; stir in 1/2 cup butter and next 3 ingredients. Cover and set aside. (If grits stiffen while shrimp mixture cooks, stir in a little milk before serving.)
Brown sausage in a large heavy skillet over medium-high heat. Remove sausage from skillet, draining oil, and set aside.
Melt 1 tablespoon butter in skillet over medium-high heat. Add garlic and green onions; sauté 1 minute. Stir in sausage, cream, and shrimp. Cook 4 minutes or until shrimp turn pink. Stir in wine, salt, and pepper. Serve with Vidalia Mustard Greens over grits.