Cook the grits. Bring 4 cups whole milk to a boil in a sauce pan, then whisk in 1 cup grits, cover, reduce heat to a simmer and cook according to package directions. If using quick cook grits, this will take 5-10 minutes. If using stone ground grits, this will take about 30 minutes.
Finish with cheddar cheese. When grits are fully cooked, add 1 cup grated white cheddar cheese, 2 Tbsp butter, ¼ cup heavy cream, and ¼ tsp salt. Whisk until creamy, then stir in scallions. Cover and set aside. Grits will thicken as they sit.
Season shrimp. In a large bowl, season shrimp with ½ tsp salt, ¼ tsp pepper, and 1 tsp paprika, then toss to thoroughly coat.
Cook the sausage. Heat 2 Tbsp butter in a skillet over medium-high heat. Add cubed andouille sausage and cook until brown on all sides, about 3-5 minutes. Next, add 2 cloves minced garlic and cook 1 minute more.
Sauté the shrimp. Add shrimp to the skillet and cook about 2-3 minutes, just until bright pink on both sides.
Make the sauce. Pour in ¾ cup stock or wine (or a combination of the two), then deglaze the pan by scraping any brown bits off the bottom with a wooden spoon. Allow sauce to reduce and thicken, about 2 minutes. Squeeze the juice from half a lemon into the sauce, taste, and adjust seasoning as necessary.
Finish, then serve. Place heaping spoonfuls of grits in a large bowl, then top with shrimp, andouille, and sauce. Garnish with scallions and chopped parsley. Serve immediately!