Combine the milk and water in a large saucepan and add the salt. Bring to a boil over medium-high heat, watching to take care that the liquid does not boil over. Whisk in the grits and bring to a boil, whisking often, then lower the heat to a gentle simmer. Cook, partially covered and stirring often, until the grits are very tender, adding more water if the grits get too thick before they are tender, 45 to 60 minutes. You may need to stir more frequently near the end of cooking so that the grits do not stick to the bottom of the pan. Add the pepper, cheese, and butter and stir to combine. Serve immediately.