Put the sugar and yeast into a bread bowl, and pour in the milk. Let this sit for 5–10 minutes, until it’s bubbled a bit and increased in volume. Add whole wheat flour, potato flakes, salt, and butter, and beat vigorously. Add unbleached bread flour a handful at a time, stirring with dough whisk after each addition, and continuing until you have a dough that just holds its shape. The dough should still be very wet. Knead in the bowl, using a flexible dough scraper as needed, and adding a little more flour if needed.

Roll the dough out of the bowl for a moment. Scrape down sides of bowl and lightly oil it, then return the dough to the bowl, flip the dough ball over so that some oil is transferred to the top of the dough, and cover loosely with plastic wrap. Let rise in a warm place for an hour, or until it is almost doubled in bulk. In the meantime, lightly beat the egg in one small bowl and put the sesame seeds in another.

Turn the dough onto a lightly greased surface, gently deflate it, and divide it into pieces. (24 pieces of about 1 ¹/₂ ounces each will give you slider rolls; 16 pieces of about 2 ounces each will give you small burger rolls; 8 pieces of about 4 ounces each will give you giant burger rolls.) Shape each piece into a long cylinder, then tie that into a knot with the two ends joined underneath. Or, roll each piece into a ball. Dip the nice side of each roll into the beaten egg, and then into the sesame seeds. Turn right-side up and place onto lightly oiled pans, with plenty of space between the rolls. Gently flatten each.

Cover and let rise until buns have almost doubled in size, about 60 minutes. Uncover the pans, place in oven, and turn oven on to 375°. Bake until light golden brown, and internal temperature is at least 190°. Transfer to a rack and let cool. Enjoy!