• Before you begin, note that this dough requires 5-8 hours of resting at room temperature followed by a 12+ hour overnight fermentation in the refrigerator. I recommend preparing the dough in the morning or early afternoon, allowing it to rise before moving it to the fridge for an overnight ferment, and then baking the buns the next day.
• In the bowl of a stand mixer (see note if making by hand) combine sourdough starter, water, olive oil, honey, egg, bread flour, and salt. Stir until a shaggy dough forms and no dry flour streaks remain. If kneading by hand, stir with a wooden spoon or spatula until combined.
  ⅔ cup (150 g) active, 1 ¼ cup (295 ml) warm water, 2 Tablespoons (30 ml) olive oil, 2 Tablespoons (42 g) honey, 1 large egg, 4 cups (500 g) bread flour, 2 teaspoons (13 g) table salt
• Switch to the dough hook attachment and knead the dough on low speed for 5-10 minutes, until dough is smooth and elastic but still slightly tacky. Add additional flour only as needed, about 1 Tablespoon at a time. If kneading by hand: transfer to a clean lightly floured surface and knead by hand for 10-15 minutes, adding flour as necessary but sparingly so the dough remains soft. Return dough to mixing bowl.
• Cover mixing bowl with plastic wrap and allow the dough to rise at room temperature until nearly doubled in size (about 5-8 hours), then transfer to the refrigerator to rest overnight.

The next day:

• Prepare two baking sheets by lining with parchment paper. Set aside.
• Remove the dough from the refrigerator and turn it out onto a clean, lightly floured surface. Divide into 10 even pieces (approximately 100g per roll). Shape each piece into a smooth ball (the dough may be sticky at this stage, this is fine), pulling the surface taut and pinching the seam closed underneath to create tension on the surface.
• Place buns onto prepared baking sheets, spacing about 2” (5cm) apart. Cover with a lightly oiled piece of plastic wrap or parchment paper (oil-side facing the buns) and let rise at room temperature until noticeably puffed, about 1-2 hours.
• Once dough is nearly finished rising, preheat oven to 375F (190C). Prepare an egg wash (if using) by whisking together egg and water until combined.
  1 egg, 1 teaspoon water
• Use a pastry brush to brush each burger bun all over the surface with egg wash (if using), then sprinkle with sesame seeds if desired.
  Sesame seeds
• Bake one tray at a time in the center rack of your 375F (190C) preheated oven for about 15 minutes, until rolls are beginning to deepen in color and the internal temperature when temped with an instant read thermometer reads between 190-195F (88-90C). Allow to cool then slice and use as desired.