Roast a large sweet potato at 400F for 55 to 65 minutes, until completely tender. Scoop out the flesh, mash it smooth, and spread it on a plate to cool to room temperature.

In a stand mixer, combine the warm milk, sugar, instant yeast, egg and cooled sweet potato mash. Add the flour and salt and mix on low until a shaggy dough forms.

With the mixer running, add the softened butter one tablespoon at a time. Knead on medium for 8 to 10 minutes, until the dough is soft, smooth and just barely tacky.

Cover and rise in a warm spot for 1 hour to 1 hour 15 minutes, until doubled.

Turn the dough onto a lightly floured counter and roll it to an even ½ inch thick. Cut 16 rounds with a 3 inch cutter, pressing straight down without twisting. Re-roll the scraps once.

Press a crease slightly off center across each round with the handle of a wooden spoon. Brush the whole round with melted butter, then fold the larger half over the smaller so the top edge overhangs by about ¼ inch. Press the seam lightly.

Arrange the folded rolls in a buttered 9x13 inch pan with all the seams facing the same direction, crowded so they touch. Cover and proof 35 to 45 minutes, until puffy.

Brush with the egg wash and bake at 350F for 20 to 25 minutes, until the tops are deep gold.

Brush the hot rolls with the remaining melted butter and sprinkle with flaky salt. Rest 10 minutes before pulling them apart.