- To make grits, combine milk with water, butter, and salt in a large saucepan over medium-high heat. Bring to a roaring boil and slowly whisk in the grits. Decrease the heat to medium low. Continue whisking until no lumps remain, about 12 minutes. Decrease the heat to low. Cover the pan and let the grits simmer while preparing gravy.
- To make gravy, cook sausage in a medium skillet over medium heat until evenly browned and cooked through, about 8 minutes. Remove sausage to a plate and cover with aluminum foil to keep warm.
- Remove excess fat from the pan, leaving just enough to coat the bottom of pan with a thin layer. Sprinkle flour over the fat in the pan and cook until toasted and brown, about 3 minutes.
- Gradually whisk in 3 cups of milk and stir until liquid begins to bubble and thicken. Let gravy bubble briefly over medium-low heat for a minute or two, stirring only occasionally to keep it from scorching, until it thickens to a rich gravy consistency. Thin with more milk until gravy just coats a spoon.
- Season generously with about ½ teaspoon black pepper and a pinch of salt. Stir in mustard greens until they just wilt.
- To serve, remove grits from heat and stir in cheese. Divide among four shallow bowls, spoon gravy on top of each, and sprinkle paprika on top. Serve hot.