Add grits and water to a medium saucepan with a lid and heat over medium heat, stirring frequently with a fork to prevent clumps. Once the mixture starts to boil, turn the heat to medium-low, add a cover to the pan, and cook for 6 minutes. Then remove from heat, add the cheese and salt, stir, and cover. Continue to stir every couple of minutes while you prepare your shrimp.
For the shrimp, heat a large nonstick skillet over medium heat. Add the butter and then the shrimp in a single layer. Cover and cook for 4 minutes. Then remove the cover, stir the shrimp, cover and cook for another minute or until shrimp is almost cooked. Add the barbecue sauce to the shrimp and heat through, about another minute.
Stir the grits again before serving, ensuring that all of the cheese is mixed through. Then serve with the shrimp and green onions.