Scald the milk (bring just under a simmer, to the point a few bubbles are forming around the edge of the pan) with the salt in a saucepan over medium heat.

Slowly whisk in the grits and continue whisking until the mixture barely simmers.

Cook, whisking often, until very thick, about 5 to 6 minutes, turning down the heat if grits are sputtering. Remove from the heat and stir in the cream or additional milk then add cheese in small handfuls until melted and smooth. Serve immediately.