In a large saucepan, bring the broth, milk, butter, and a pinch of salt and pepper to a boil. Stir in the grits. Reduce the heat to a simmer. Cover with a lid and cook for about 10 minutes or until thickened, stirring occasionally. Stir in the cheese and set aside with a lid to keep warm.
In a large nonstick pan on medium heat, heat the oil. Sauté the shrimp, garlic, and seasoning in the pan until the shrimp turn firm and pink and no longer translucent. Serve the shrimp over grits and sprinkle with chopped green onions to garnish.