To make the bun dough: Combine all of the dough ingredients in the bowl of a stand mixer fitted with the dough hook.  Mix, starting on low speed, and gradually increasing the speed to medium, until a soft dough is formed, about 5 minutes.  It will still be slightly sticky, but should pull off the side of the bowl when kneaded.  Turn the dough onto a lightly floured surface and bring into a ball by hand, kneading a few times until the dough is no longer sticky.  Place in a lightly greased bowl, covered with a towel, to rise in a warm place for an hour; the dough will be doubled in volume.

Turn the dough out onto a lightly floured surface and flatten slightly to form a rough rectangle.  Cut into 6 pieces, each weighing approximately 3-1/2 to 4 ounces.  Roll each piece into a ball and place on a parchment-lined baking sheet or in a greased hamburger bun pan, flattening the dough slightly with your hand.  Cover with a towel and allow to rise in a warm place until doubled in volume, approximately 30 minutes.

Mix together the sesame seeds and a generous pinch of flaky sea salt in a small bowl.  In a separate mixing bowl, combine the egg and water thoroughly so it is a homogenous mixture.  With a pastry brush, gently pat the egg wash on the top and sides of one bun; use the side of your mixing bowl to remove the excess egg wash from the brush before doing this.  Generously sprinkle the sesame seed mixture all over the bun.  Repeat with the remaining buns.

Towards the end of the proofing time, preheat the oven to 375°.  Bake the buns for 15 to 18 minutes, until they are golden brown and the sesame seeds are lightly toasted. Cool on a wire rack.