In a large, heavy pot, heat the olive oil over medium-high heat. Add the onions, bell pepper, celery, salt, black pepper, and cayenne. Cook, stirring, until the vegetables are soft and lightly golden, about 4 minutes. Add the sausage and ham and continue to cook, stirring occasionally, for 2 minutes. Add the garlic and tomato and cook for 2 minutes. Add the milk and bring to a boil. Reduce the heat to medium and stir in the grits. Stir for 2 minutes, then add the shrimp. Cook, stirring, until the grits are tender and creamy, 7 to 8 minutes. Stir in the green onions, then add the cheese and stir until it is completely melted, about 30 seconds.
Serve hot right from the pot.
Yield: 8 appetizer servings or 4 main-course servings