To prepare buns, in the bowl of a standing mixer with a paddle attachment, combine flour, sugar, yeast and salt.
In another bowl, warm milk and butter in a microwave or stove top, until butter is melted and just warm to touch, about 110F.
Stir in the egg and sweet potato puree to combine.
Add milk mixture to the flour mixture, and mix until combined.
Switch to the dough hook and knead the dough on low speed until smooth and elastic, about 8 minutes. Form the dough into a ball and transfer it to an greased bowl, cover it with a tea towel and let sit in a warm place for an hour to rise.
When the dough is risen, move the dough to a lightly floured surface. Roll to flatten the dough into a big rectangle, about 12 x 11-inch.
To make the filling, pour the melted butter over the surface of the dough. Use your fingers to spread the butter evenly.
Combine the brown sugar and cinnamon. Sprinkle the cinnamon sugar over the butter.
Beginning at the end farthest from you, roll the long side of the rectangle tightly toward you. Pinch the seam together at the end.
Slice it into 1 1/2-inch slices. Place the sliced rolls in a well greased baking pans, one inch apart. Cover and allow to rise in a warm place for 30 minutes.
Preheat oven to 350F. Bake the rolls for 20 to 25 minutes, until golden brown.
To prepare the glaze, mix all the ingredients and whisk until the mixture becomes thick and smooth. Generously drizzle the glaze over the hot rolls. Serve warm or in room temperature.