Warm milk and ¼ cup butter until butter melts, cool to 110°F, then whisk with yeast and sugar in a stand mixer bowl. Let sit 5 minutes until foamy, then stir in sweet potato and egg.

Add 3 cups flour and salt, mix on low, then knead with dough hook 6 minutes, adding remaining flour a tablespoon at a time until dough is smooth, elastic, and slightly tacky.

Place dough in a greased bowl, cover, and let rise in a warm spot for 1 to 1 ½ hours until doubled.

Punch dough down, roll into a 16x12-inch rectangle. Spread ½ cup soft butter almost to the edges, sprinkle evenly with brown sugar and cinnamon, and roll up tightly from the long side. Slice into 12 rolls and place in a buttered 9x13-inch dish.

Cover and let rise 30 to 45 minutes until puffy and touching, then preheat oven to 350°F (175°C). Bake uncovered for 20 to 25 minutes until deep golden brown and set in the center.

Beat cream cheese, 2 tablespoons butter, powdered sugar, and vanilla together. Thin with milk to pourable consistency, then spread over warm rolls. Serve right away.