Melt butter in a large skillet over medium heat; gradually whisk in flour, and cook, whisking constantly, until flour is a light caramel color (about 6 minutes).
Add onion, bell pepper, and celery, and cook 8 to 10 minutes or until tender. Add sausage, and cook 2 minutes. Stir in chicken broth, salt, and pepper, stirring to loosen particles from bottom of skillet. Bring to a light boil over medium-high heat. Reduce heat to medium, and simmer 8 to 10 minutes or until slightly thickened.
Stir in shrimp, cream, and green onions, and cook, stirring occasionally, 3 minutes or just until shrimp turn pink. Serve over Creamy Cheddar Cheese Grits.