Add the water or milk, grits, and salt to a medium saucepan, off the heat, and stir. Let sit until the grits have settled to the bottom and chaff has risen to the top, about 5 minutes. With a small, fine-mesh strainer, skim chaff from the top of the liquid and discard.
Place over medium-high heat and bring the water to a simmer while whisking gently but constantly. Continue to simmer and whisk until the grits have released enough starch so that the individual particles are suspended, 5 to 7 minutes. Reduce the heat to low, cover, and cook, stirring every 5 minutes, until the grits are cooked, about 1 hour.
Remove from the heat, whisk in butter and cover until ready to serve. You can let it sit this way for up to 1 hour before serving. If held longer than 1 hour, you will need to add warm water, 1 tablespoon at a time, to loosen up the grits.