In the bowl of a stand mixer with a mixing paddle, add 1 cup of the bread flour, yeast, sugar, and salt. Stir to combine.
Add the water to the flour mixture and stir. Stir in the melted butter, 1 whole egg, and 1 egg yolk. reserve the egg white for the egg wash. Mix until combined.
Swap out the mixing paddle for a dough hook. Gradually add the remaining flour until soft ball forms. The dough should not be sticky and will pull away from the side of the mixing bowl. Continue to knead the dough until it is soft and smooth.
Clean the mixing bowl and lightly coat it with oil or cooking spray. Add the dough to the mixing bowl and cover with plastic wrap. Allow the dough to rise 1-2 hours, or until doubled in size.
Punch down the dough and divide the dough into 8 pieces. Roll the dough pieces out into a ball shape then flatten with the palm of your hand.
Place the roll on a baking sheet lined with a Silpat or with sheets of parchment paper. Allow the hamburger buns to rise for 1 hour, or until doubled in size.
Preheat the oven to 375 degrees. Whisk the remaining egg white until frothy. Brush the burger buns with the egg wash and then sprinkle with the desired topping.
Bake the buns for 15 minutes, or until golden brown.