Add all the buns ingredients to a large mixing bowl, and mix until combined. Then continue to knead with a dough hook or by hand for 5-10 minutes, until the dough is smooth. The dough should be tacky, but not sticky. If it's too sticky, add 2-4 additional tablespoons of flour one at a time, mixing in between each addition.
Cover the dough and set it aside for 1-2 hours in a warm place, until it has risen significantly.
Divide the dough into 8 equal pieces, and shape to your liking. For hamburger buns, shape the pieces into balls, and then flatten the balls slightly, until they are about 1" thick. For hotdog buns, shape the pieces into logs about 6-7" long, and flatten slightly.
Place your buns on a greased or parchment-lined pan, and cover with a tea towel or lightly with plastic wrap. Allow to rise a second time, for 30 minutes-1 hour until puffy.
Preheat the oven to 375℉. Brush the tops of the buns with the egg and water whisked together, and then sprinkle the sesame seeds on top. Bake for 15-20 minutes, until they are golden and reach an internal temp of 190℉.
Allow to cool on a rack fully before cutting or serving.