Prepare Grits: Preheat oven to 350°. Brink milk, 1/4 cup butter, and 4 cups water to a boil in an ovenproof Dutch oven over medium-high heat. Whisk in grits; bring mixture to a boil, whisking occasionally. Cover and bake 45 minutes or until the grits are creamy, whisking every 15 minutes.
Meanwhile, melt 1 tablespoon butter in a large skillet over medium heat; add 4 garlic cloves and 3 shallots, and saute 3 1/2 minutes or until the shallots are translucent.
Add wine, stirring to loosen particles from the bottom of the skillet. Cook, stirring often, 4 minutes or until the liquid is reduced by two-thirds; fold into hot cooked grits. Stir in cheese and the next 3 ingredients.
Prepare Shrimp Sauce: Peel shrimp and devein. Sprinkle shrimp with 1/8 teaspoon each salt and pepper.
Cook shrimp, in 2 batches, in 2 tablespoons hot oil in a large skillet over medium-high heat for 2 minutes on each sidem or just until the shrimp turns pink and forms a "C". Remove shrimp from the skillet.
Saute 3 garlic cloves and 1 tablespoon minced shallots in the remaining 2 tablespoons hot oil in the skillet over medium-high heat for 1 minute. Add tomatoes and the next 4 ingredients. Cook, stirring often, 5 to 7 minutes or until the tomatoes begin to break apart. Remove from heat. Stir in shrimp and 3 tablespoons butter. Serve over grits with chives.