Heat 2 cups each of stock and milk in a heavy-bottomed saucepan until just simmering. We used shrimp stock made from the shells of the shrimp we planned to serve with the grits.
If your grits have chaff, you'll need to remove it. While milk is heating, put grits in a large mixing bowl and cover with cool water. Stir grits aggressively so the chaff floats to the top. Skim the surface carefully to remove the chaff. Drain the grits in a fine strainer and slowly add them into the simmering water and milk, stirring constantly.
Cook, stirring often to keep them from sticking and scorching, until the grits are tender to the bite and have thickened to the consistency of thick oatmeal. Stone-ground grits may require an hour or more to cook and may require the addition of more milk during cooking. Typically we're happy with our stone-ground grits in about thirty minutes and regular grits in about twenty.
Season grits generously with salt. Stir in cream, butter, and cheese until completely melted.
Remove from heat and let rest, covered, until serving. Serve hot.