Preheat oven to 400°F. Wrap sweet potato in foil. Roast until tender, 35–45 minutes. Let cool.
In a saucepan, bring broth and milk to a simmer.
Rinse grits thoroughly three times.
Whisk grits into simmering liquid. Cook, whisking often, until thick and creamy, 25–30 minutes.
Mash cooled sweet potato (about 2 cups). Stir into grits. Blend until smooth.
Stir in butter. Season with salt and pepper.
Serve topped with a pat of butter and black pepper.