Combine 4 cups water (or half water, half milk) with 1 tsp salt in a medium saucepan; bring to a rolling boil over medium-high heat.

Slowly pour 1 cup stone-ground polenta into boiling liquid, whisking constantly to prevent lumps until mixture thickens (about 1–2 minutes).

Reduce heat to low; cook polenta, stirring frequently with a wooden spoon, until creamy and tender, 20–25 minutes, it will pull away from the sides.

Remove pan from heat; stir in 2 tbsp butter and 1 cup freshly grated Parmesan until melted and fully combined.

Pour in 1/4 cup heavy cream (or milk), stirring until the polenta is silky smooth and reaches your desired consistency.