Preheat oven to 350 degrees and grease an 11X7-inch casserole dish.
Melt butter in a large skillet over medium-high heat. Add onion, bell pepper, and jalapeno and cook until crisp-tender, about 3 minutes.
Add garlic and sausage and cook until sausage is browned.
Add tomatoes, shrimp, cajun seasoning, and green onions and cook just until shrimp turned pink. They will cook more in the oven so be careful not to overcook them. Remove from heat.
In a medium pot, bring chicken broth and water to a boil. Add salt and gradually stir in grits. Cook stirring frequently, for 5 minutes.
Place eggs in a small bowl. Gradually whisk in about 1 cup of the hot grits to temper the eggs. Add the egg mixture to the pot and whisk into the rest of the grits.
Stir shrimp mixture and 1 cup of cheese into the grits and pour into prepared pan. Top with remaining cheese and bake for 40 minutes.