Place the milk, water, and salt into a large, heavy-bottomed pot over medium-high heat and bring to a boil. Once the milk mixture comes to a boil, gradually add the cornmeal while continually whisking. Once all of the cornmeal has been incorporated, decrease the heat to low and cover. Remove lid and whisk frequently, every 3 to 4 minutes, to prevent grits from sticking or forming lumps; make sure to get into corners of pot when whisking. Cook for 20 to 25 minutes or until mixture is creamy.
Remove from the heat, add the pepper and butter, and whisk to combine. Once the butter is melted, gradually whisk in the cheese a little at a time. Serve immediately.