Combine all dough ingredients in the bowl of a stand mixer fitted with a dough hook (and also use a bread machine, hand mixer, or knead by hand). Mix on low until a smooth dough forms. Depending on your pumpkin purée, you may find your dough is too wet. If dough is too wet, add more flour in 2 Tablespoon increments.
Place the dough in a clean, lightly greased bowl and cover with plastic wrap. Let rise for 60-75 minutes until nicely puffy.
Transfer dough to a lightly greased surface and divide into 16 pieces. Form each piece into a roll, crease side down.
Cut four 10-inch pieces of kitchen twine for each roll; you'll need a total of 64 pieces of twine. Lightly soak in vegetable oil. Lay four pieces of twine in a star shape, overlapping in the middle point. Place a sage leaf at the center of the star, then add the dough ball, crease side up (remember, you're making these upside down).
Tie the opposite ends of each string together across the roll, squeezing the dough. Once all strings are tied, trim the excess string and flip over so the tied ends are under the roll.
Place each tied roll on a baking sheet lined with parchment paper or silpat mats. Cover with plastic wrap and allow to ruse for 1 ½ to 2 hours, until puffy.
Preheat the oven to 350°F. Uncover the rolls and brush with egg wash. Bake for 25 to 30 minutes, or until golden brown.
Remove from the oven, brush with melted butter and add a sprinkle of flaky sea salt. Allow to cool for at least 10 minutes (until cool enough to handle), then cut the strings on the top of the roll. Turn over, and pull out the knotted ends of the strings. Keep in mind you will not see the bottom of the rolls! They don't need to be beautiful!
Once strings are removed, the rolls are ready to enjoy!