Step 1

Preheat oven to 350°F. Heat 2 tablespoons of the butter in a 12-inch cast-iron skillet over high until foamy. Add ham, bell peppers, and mushrooms. Cook, stirring occasionally, until vegetables are soft and mixture is lightly browned, about 8 minutes. Transfer mixture to a plate, and wipe skillet clean.

Step 2

Bring 6 cups of the milk to a boil in a large saucepan over medium-high. Whisk in grits, reduce heat to medium, and cook, whisking often, until thickened, about 7 minutes. Remove from heat, stir in salt, pepper, and 2 cups of the cheese.

Step 3

Whisk together eggs and remaining 1/2 cup milk in a large bowl. Add 1/2 cup grit mixture at a time, whisking between each addition (mixture will be lumpy). Stir ham mixture into egg-grits mixture until combined.

Step 4

Melt remaining 2 tablespoons butter in iron skillet over medium until foamy. Add omelette mixture to skillet. Top with remaining 1 cup cheese. Bake in preheated oven until set and top is golden, 30 to 35 minutes. Let stand 10 minutes. Cut into wedges. Sprinkle with chives.