1. Heat olive oil in a large skillet over medium-high heat. Add tasso; sauté 2 minutes or until edges are golden. Add onion; sauté 2 minutes. Add garlic; sauté 1 minute. Add shrimp to pan, sprinkle with Cajun seasoning, and cook 3 minutes, turning once. Add 1/4 cup water, scraping pan to loosen browned bits. Remove from heat; add butter, stirring to melt. Cover and keep warm.
2. Bring milk, salt, and 2 cups water to a boil over medium-high heat. Reduce heat. Gradually add grits, and cook until thick and bubbly (about 5 minutes), stirring constantly with a whisk. Remove grits from heat; add cheese, stirring with a whisk until cheese melts.
3. Spoon grits evenly onto 6 plates. Top evenly with shrimp, ham mixture, and green onions.