Meanwhile, Make the Topping:
In the same skillet, heat the milk until just warm, about 105°. Pour the warm milk into the bowl of a standing electric mixer fitted with the dough hook. Add the yeast and let stand for 5 minutes. Gently mix in the granulated sugar, light brown sugar, salt, vanilla seeds, nutmeg and rum. Add the sweet potato puree, browned butter and solids, egg and egg yolks and beat until combined. Add the 3 1/4 cups of bread flour and beat at medium speed until the dough is evenly moistened, about 2 minutes. Increase the speed to moderately high and beat until a soft dough forms, about 5 minutes. Gather the dough into a ball and transfer to a buttered bowl. Cover and let rise in a draft-free place for 1 hour.