Grits: Boil milk and gradually add grits. Turn to low and simmer for 30-45 minutes stirring frequently. Before ready to serve, add butter, cheese and extra milk if needed.
Shrimp: Season shrimp with salt and pepper. Heat butter and oil in a large sauté pan over medium-high heat until melted and foamy. Add sausage and onion and sauté until the onion is tender and the sausage is browned, 5-6 minutes.
Add the shrimp and cook for 1 minute per side. Once they are opaque, remove with a slotted spoon to a plate. Add the tomatoes to the pan with a big pinch of salt and pepper and cook, stirring, until they have softened another 3-4 minutes.
Stir in wine and reduce until almost dry, about 3 minutes. Stir in heavy cream and reduce slightly. Return the shrimp to the pan and cook for another minute.
Place grits on plate and top with shrimp and sauce. Garnish with green onions.