Preheat oven to 350°F. Grease a 13"x9" baking dish with butter or non-stick spray.
In a large skillet, cook and crumble sausage over medium heat until browned and cooked through. Drain any excess fat and set aside.
In a large saucepan, bring 4 cups of water to a boil. Stir in grits and salt, and reduce the heat to low. Cook the grits, stirring periodically, for 5-7 minutes until thickened.
Pour the melted and slightly cooled butter in a large bowl. Transfer the cooked grits into the bowl. Add the remaining seasonings, and stir until well combined.
Add 2 cups of the cheese, and stir until the cheese is melted and well combined.
Gradually stir milk into the grits mixture.
Add the eggs to a medium bowl and beat lightly with a fork. Temper the eggs by adding 2 tablespoons of the grits and whisking quickly. Repeat this process 3 times.
Stir in the tempered eggs and cooked sausage until everything is evenly combined.
Pour the mixture into the prepared baking dish. Top with the remaining shredded cheese.
Bake 35-40 minutes, or until the casserole is set and the top is golden brown.
Allow the casserole to cool for a few minutes before serving. Sprinkle sliced green onions on top, if desired.