In a medium saucepan, bring the water and kosher salt to a boil over medium-high heat.
While whisking, slowly sprinkle in the stone-ground grits to prevent lumps. Reduce heat to low so the surface barely simmers.
Cook, stirring frequently and scraping the bottom and sides, until the grains are fully tender and the texture is creamy and spoonable, 45–60 minutes. The grits should hold a soft mound and the individual kernels should be tender with just a slight bite.
Remove from heat and stir in the unsalted butter until melted and incorporated.
Season with the black pepper, cover, and let stand 5 minutes to thicken slightly. Stir and serve hot.