In a medium pot, bring 5 cups water and 1 teaspoon salt to a boil over high. Whisk in grits and cook, stirring constantly, until thickened, about 2 minutes. Reduce heat and simmer 15 minutes.
Meanwhile, in a large skillet, heat oil over medium-high. Add andouille and cook until golden, 3 to 5 minutes. With a slotted spoon, transfer andouille to a plate and reduce heat to medium. Add garlic and scallion whites to skillet and cook until fragrant, about 30 seconds. Stir in flour. Whisk in broth and cream. Cook, stirring and scraping up browned bits from skillet, until thickened, about 3 minutes. Add shrimp and andouille and cook, stirring constantly, until shrimp are opaque throughout, about 5 minutes. To serve, top grits with shrimp mixture and sprinkle with scallion greens. Serve with tomatoes if desired.