Preheat the 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. Add sausage; cook and stir until browned and crumbly, 5 to 7 minutes. Transfer sausage to a paper-towel-lined plate; discard grease.

Beat eggs and milk together in a bowl. Stir sausage, egg mixture, and bell peppers into grits mixture; pour into prepared baking dish.

Bake in the preheated oven until set, 45 to 60 minutes.