Bring water and milk just to a simmer in a 4- to 5-quart heavy saucepan. Meanwhile, cover grits with water in a large bowl and whisk vigorously. Let stand 30 seconds, then skim any chaff that has floated to surface with a fine-mesh sieve. Drain grits well in a fine-mesh sieve and whisk into simmering milk mixture.

Reduce heat to low and simmer grits, partially covered, stirring often with a heatproof rubber spatula, until grits are tender and thickened to the consistency of loose oatmeal, about an hour and a quarter. (Stir more toward end of cooking to avoid scorching). If grits become too thick before they are tender and creamy, thin with hot water (about a half cup).

Stir in cream, butter, and salt. Remove from heat and keep warm, covered, up to 20 minutes.

making ahead: Grits are at their creamiest right after they are made but can be made up to 2 days ahead. Chill, uncovered, until cool, then cover. To reheat, break congealed grits into pieces and whisk in enough boiling water to loosen (up to about 1 cup). Heat over low heat, stirring constantly.

Can't find stone ground grits? Regular grits (but not quick-cooking) may be used instead. They’ll take less than half the time to cook.