Bring water to a boil in a medium saucepan over high. Add grits and 1 teaspoon of the salt. Reduce heat to medium-low, and cook, stirring occasionally, until grits are thickened and tender, about 5 minutes. Remove pan from heat; cover and let stand 5 minutes.

Meanwhile, whisk together half-and-half, mustard, pepper, eggs, egg yolk, and remaining 1 teaspoon salt. Stir in grits and cheese until cheese is melted. Divide mixture evenly among 6 (8-ounce) lightly greased ramekins. Cover and chill 8 hours or overnight.

Preheat oven to 350°F. Uncover ramekins, and place on a baking sheet; let stand at room temperature while oven preheats, 15 to 20 minutes. Bake in preheated oven until puffed and edges are set, about 42 minutes. Let stand 10 minutes. Sprinkle with chives, and serve.