Bring 4 cups salted water to a boil in a medium pot. Slowly add the grits, stirring constantly to avoid lumps.
Add 1 teaspoon salt and partially cover. Reduce the heat to medium and cook about 15 minutes, stirring occasionally.
Uncover the pot and stir in the butter and 3 tablespoons of the cream. Continue to stir, adding the remaining cream, a few tablespoons at a time, until the mixture thickens and begins to sputter slightly, about 15 minutes. Taste and add more salt, if desired.