1. Preheat oven to 325°. Devein shrimp, if desired.
2. Bring broth and next 2 ingredients to a boil in a large saucepan over medium-high heat. Whisk in grits, and return to a boil; reduce heat to low, and stir in butter. Cover and simmer, stirring occasionally, 10 minutes or until liquid is absorbed. Remove from heat.
3. Stir together eggs and next 4 ingredients in a large bowl. Gradually stir about one-fourth of hot grits mixture into egg mixture; add egg mixture to remaining hot grits mixture, stirring constantly. Stir in shrimp until blended. Pour grits mixture into a lightly greased 11- x 7-inch baking dish.
4. Bake at 325º for 55 minutes to 1 hour or until mixture is set. Let stand 10 minutes.