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 1 1/4hours (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 1/2 cup).
Stir in cream, butter (if using), and salt.
Remove from heat and keep warm, covered, up to 20 minutes.
·If you can't find stone-ground grits, use regular grits (but not quick-cooking). Regular grits will take less than half the time to cook.·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).