Prepare Grits: Preheat oven to 350°. Bring 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 grits are creamy, whisking every 15 minutes.
Meanwhile, melt 1 Tbsp. butter in a large skillet over medium heat; add 4 garlic cloves and 3 shallots, and sauté 3 1/2 minutes or until shallots are translucent. Add wine, stirring to loosen particles from bottom of skillet. Cook, stirring often, 4 minutes or until liquid is reduced by two-thirds; fold into hot cooked grits. Stir in cheese and next 3 ingredients.
Prepare Shrimp Sauce: Peel shrimp; devein, if desired. Sprinkle shrimp with 1/8 tsp. each salt and pepper.
Cook shrimp, in 2 batches, in 2 Tbsp. hot oil in a large skillet over medium-high heat 2 minutes on each side or just until shrimp turn pink. Remove shrimp from skillet.
Sauté 3 garlic cloves and 1 Tbsp. minced shallots in remaining 2 Tbsp. hot oil in skillet over medium-high heat 1 minute. Add tomatoes and next 4 ingredients. Cook, stirring often, 5 to 7 minutes or until tomatoes begin to break apart. Remove from heat. Stir in shrimp and 3 Tbsp. butter. Serve with chives.