In a Dutch oven or large, heavy pot heat the olive oil over medium-high heat.
Add onion and green pepper and cook until soft, about 4 minutes.
Add Andouille sausage and ham and cook for 2 minutes, stirring occasionally.
Add garlic and cook 1 minute.
Add water, milk, and salt and bring to a simmer. Gradually stir in grits.
Add TABASCO sauce, Creole or Cajun seasoning, and pepper. Cook, stirring frequently for about 4 minutes.
Stir in shrimp and tomato and cook for another 3 minutes, or until shrimp are cooked through.
Stir in cheese and green onions. Serve.