Combine the milk, salt, and pepper in a small heavy saucepan and bring to a simmer over medium heat. Add the grits slowly, stirring constantly until thoroughly combined. Reduce the heat to medium-low and simmer uncovered, stirring frequently, until thickened, 12 to 15 minutes. Add the butter and stir to incorporate. Add the cheese and stir until melted.
2 Serve immediately or cover to keep warm until ready to serve, stirring occasionally.