Mix 113 g sourdough discard, 177 g warm water, 210 g all-purpose flour, 210 g bread flour, 60 g avocado oil, 60 g honey, 1 egg, and 6 g salt in a large bowl with a dough whisk until incorporated fully. It will look shaggy and possibly lumpy. Cover the bowl with a shower cap bowl cover. Rest for 30 minutes.
Do 2-3 rounds of stretch and folds, 30 minutes apart. Wetting your hands with water will make it less sticky. See Notes for more information about stretch and folds.
Let dough sit on counter, covered, for 8-12 hours, or until doubled in size. Put it in the fridge to chill overnight.
The next day, divide the dough. For mini sliders (as pictured), divide into 18 small balls, weighing about 50g each. For regular-sized buns, divide into 9 balls, weighing about 100g each.
Shape each dough ball and set on a parchment-covered sheet tray. To shape: One piece at a time, right on your work surface, pull the outer edges up and towards the center of the dough, all around. Gently pinch the pulled edges together. Turn the ball over so that the seam side is facing down on your work surface. Roll it around a little bit to smooth out the bottom.
Cover the sheet tray with a towel and let rest on the counter for about 2 hours.
Preheat oven to 350°F (175°C). Whisk 1 egg with a Splash of water and brush the egg wash on each bun. Sprinkle sesame seeds on top.
For mini sliders, bake for about 18 minutes, rotating the sheet tray halfway through. For regular sized buns, bake for 20-25 minutes, also rotating the sheet tray halfway through. Enjoy!
Notes
Stretch and folds: One round of stretch and folds means you grab some of the dough in your hand, stretch it up, and lay it back down over the rest of the dough ball. You then rotate the bowl a quarter turn and do it again. You will do this a total of four times, essentially rotating the bowl one-quarter turn per stretch and fold to ensure you stretch all of the dough. This helps develop the gluten.
During shaping: I sprinkled flour on the dough and my work surface during this process to keep the dough from being too sticky.