Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.
Bring water, half-and-half, and salt to a boil in a saucepan; slowly whisk in grits. Reduce heat to low and simmer, stirring occasionally, until thick, about 20 minutes. Stir in Cheddar cheese and butter until melted. Cool.
Heat a large skillet over medium-high heat. Cook and stir sausage in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease.
Beat eggs and milk together in a bowl. Stir sausage, egg mixture, orange bell pepper, and red bell pepper into grits mixture. Pour grits mixture into prepared baking dish.
Bake in the preheated oven until set, 45 to 60 minutes.