In a small bowl, combine water, yeast, and sugar. Set aside for 10 minutes until mixture becomes foamy.
In a stand mixer combine yeast mixture, egg, butter, and salt. Mix together with dough hook attachment until well combined. Add flour a little at a time while mixing. Dough will start pulling away from the sides of the bowl, but will still be quite sticky. Mix 3 more minutes. Dough will start pulling away from the sides of the bowl, but will still be quite sticky. Beat 3 more minutes. Push down with a spatula and/or add a little more flour if needed. Coat another large bowl with 2 tablespoons oil. Take dough out of mixing bowl and place in oiled bowl, turning over once to coat all over. Place clean towel or plastic wrap over bowl and let raise in a warm spot for 1 hours or until doubled in size.
Put dough out onto a lightly floured surface and lightly roll or pat dough down into an even rectangle (about 1" thick). Cut dough into 8 even pieces and gently form into a disc shape, pulling and tucking the edges underneath (about 1/2" thick).
Space dough discs 1" apart on a parchment-lined baking sheet. If you don't want them to touch after rising and/or baking (to make perfectly round buns instead of having to pull them apart a little), you can put a couple on a separate sheet. Spray the buns with cooking spray, then spray a sheet of plastic wrap and gently place the plastic wrap over the dough, making sure they are all covered. This will prevent the wrap from sticking to the dough as they rise. Place dough in a WARM place to rise. After the dough has risen to bun-size (about 1 hour), carefully remove the plastic wrap. Heat oven to 350-degrees.
Optional: In a small bowl, beat the egg until foamy. Using a pastry brush, GENTLY brush the egg wash over the buns. Sprinkle sesame seeds over the buns (see other topping options above).
Place buns in the heated oven and bake for 15 minutes or until the tops start to turn golden brown. Remove from the oven and cool before serving. Cut lengthwise to serve as a hamburger bun.