In the bowl of stand mixer fitted with the dough hook attachment, combine the warm water, sourdough discard, dry active yeast, granulated sugar, avocado oil, and the large eggs. Use a whisk to thoroughly combine all of the ingredients together.

With the mixer on low speed, slowly add the flour and salt to the bowl. Mix the dough for 8-10 minutes on medium low speed. The dough will be quite tacky and will still stick to the sides of the bowl, that is ok!

Cover the bowl with plastic wrap, or a disposable shower cap, and let the dough rise at room temperature for about an hour until it has doubled in size.

Line a rimmed baking sheet with parchment paper, set aside. Pour the dough out onto a well floured work surface, and use a bench scraper to divide the dough into 10 equal pieces.

With lightly floured hands, shape the buns: bring the edges of each piece of dough into the center, and pinch together creating a round circle. Place the ball of dough onto the work surface, seam side down. Use the palm of your hand and fingertips to roll the dough around in a circle. Place the shaped bun onto the prepared baking sheet. Repeat with the rest of the pieces of dough.

Use the palm of your hand to flatten out the buns slightly into a disk for that signature hamburger bun look.

Lightly dust the tops of the buns with flour, and loosely place a clean tea towel over the buns. Let them rise at room temperature for about 1 hour until they are puffy. Preheat the oven to 350℉.

Brush the tops of the risen hamburger buns with the beaten egg, and generously sprinkle the sesame seeds on top. Bake the buns for 25-27 minutes until they are deeply golden brown. Allow the buns to cool for at least 20 minutes before slicing. Enjoy with any of your favorite burgers, chicken sandwiches, egg or tuna salad sandwiches, or even a pressed panini sandwich.