1. Peel shrimp, reserving shells; devein shrimp, if desired. Bring shells and 4 cups water to a boil in a medium saucepan over medium-high heat; reduce heat to low, and cook 20 minutes. Pour shrimp broth through a colander over a large bowl, pressing shells with back of a spoon; discard shells.
2. Heat oil in a Dutch oven over medium heat; stir in flour, and cook, stirring constantly, until flour is caramel colored (about 8 to 10 minutes). Add onion and next 3 ingredients, and cook, stirring often, 5 to 7 minutes or until tender. Stir in 2 cups shrimp broth, tomato paste, and next 4 ingredients. Reduce heat to low, and cook, stirring occasionally, 45 minutes. Add shrimp, and cook 10 minutes, stirring in 1/4 to 1/2 cup remaining shrimp broth to reach desired consistency.
3. Meanwhile, bring milk, 2 1/2 cups water, and salt to a boil in a saucepan over high heat. Gradually stir in grits. Reduce heat to low, and simmer, stirring occasionally, 10 to 12 minutes or until thickened. Serve Creole Shrimp over grits.