Bring whole milk to a boil in a sauce pan, then whisk in grits, cover, reduce heat to a simmer and cook according to package directions.
When grits are fully cooked, add grated white cheddar cheese, butter, heavy cream, and salt. Whisk until creamy, then stir in scallions. Cover and set aside.
In a large bowl, season shrimp with salt, pepper, and paprika, then toss to thoroughly coat. Heat butter in a skillet over medium-high heat. Add cubed andouille sausage and cook until brown on all sides. Next, add cloves minced garlic and cook.
Add shrimp to the skillet and cook, just until bright pink on both sides.
Pour in stock or wine, then deglaze the pan by scraping any brown bits off the bottom with a wooden spoon. Allow sauce to reduce and thicken. Squeeze the juice from half a lemon into the sauce, taste, and adjust seasoning as necessary.
Place heaping spoonfuls of grits in a large bowl, then top with shrimp, andouille, and sauce. Garnish with scallions and chopped parsley.