In the bowl of your stand mixer whisk together the warm water, sourdough starter, honey, one egg, and melted butter.
Add the flour and salt to the wet ingredients. Using the dough hook on your mixer, knead the dough for 8-10 minutes. The dough will be glossy, smooth and slightly sticky.
Grease a mixing bowl with butter. Transfer the dough to the mixing bowl, cover with plastic wrap and let rise for 6-8 hours or until almost double in size.
Transfer the dough to the refrigerator to chill overnight.
The next morning dump the dough ball out onto a clean work surface. Divide the dough into 8 equal portions. I like to use a scale to weigh and then divide the dough. Roll each dough into a ball and set on a baking sheet lined with parchment paper.
Use the flat of your palm to flatten each hamburger bun. Cover with plastic wrap or a damp tea towel and let sit for 2-4 hours or until puffy: the dough should double in size.
Preheat the oven to 325 degrees F. Mix the egg yolk with one tablespoon of water and brush the tops of the buns with the egg yolk mixture. Sprinkle sesame seeds or bagel seasoning on top if desired.
Bake for 25-28 minutes or until the tops are golden brown. Enjoy!