Measure warm water into a glass measuring cup with a pour spout. Sprinkle the yeast and a pinch of the sugar over the water's surface. Stir to dissolve the yeast and set aside.
Melt 6 tablespoons of the butter in a small sauce pan over low heat. Add milk, sugar, and salt. Stir over low heat until the sugar dissolves. Remove from heat and set aside.
With the paddle attachment, beat the sweet potato and egg in the bowl of a standing electric mixer. Beat in the milk mixture and then add the activated yeast (it should be bubbly). Mix to combine.
Add 2 cups of the flour and mix well. Add the remaining flour, about 1/4 cup at a time, allowing it to incorporate before adding more. The dough will be quite sticky.
Switch to the dough hook and knead until the soft dough looks smooth, about 5 to 7 minutes.
Scrape the soft, tacky dough into a greased bowl, flipping it once to coat the dough with oil. Cover the bowl with plastic wrap and let the dough rise in the refrigerator overnight. It should double in size.
Grease or parchment-line a rimmed baking sheet (I used a 10 by 15-inch pan). Turn the cold dough out on a lightly-floured surface and divide it into 24 evenly-sized pieces.
Using just enough flour to prevent sticking, roll each piece into a tight ball and place it on the prepared baking sheet, spacing the rolls closely together.
Cover the rolls with lightly oiled plastic wrap and let them rise at room temperature for 1 to 1 1/2 hours.
In the meantime, preheat oven to 375°F.
Bake the risen rolls for 15 to 20 minutes, until golden brown and gently firm to the touch.
While the rolls bake, melt the remaining 2 tablespoons butter. Brush oven-warm rolls with the melted butter.