Pour the sourdough starter into a large bowl. Add the water and honey, and whisk until the starter is fully dissolved in the water.
Add in the melted butter and egg, and whisk again until fully incorporated.
Add both flours and the salt to the bowl, and use a spoon to lightly mix everything together until a shaggy dough forms. The dough will be sticky and not very pretty. That's ok. Rest the dough for 30 minutes at room temperature so the flour can fully hydrate, making the next step much easier.
After 30 minutes, perform the first series of stretch-and-folds to build the structure of the dough. This is essential to strengthen the gluten and achieve a good rise. Simply grab a corner of the dough, stretch it up and away from the bowl, and fold it across to the other side. Turn the bowl 90 degrees, and repeat the stretch-and-fold about 6 more times, turning the bowl each time. The dough will become stronger and less stretchy the more you fold it. Loosely cover the bowl with a towel or plastic wrap. Repeat the stretch-and-fold process every 30 minutes over the course of 2 hours, for a total of 4 stretch-and-folds.
After the fourth and final stretch-and-fold, loosely cover the bowl with a towel and rest the dough at room temperature for about 4 hours, or until just about doubled in size.
Meanwhile, line a baking sheet with parchment paper, and set aside. If you're using metal rings to help keep the shape of the buns, lightly grease the insides with butter or avocado oil and space them out on the baking sheet. Now it's time to shape the dough into the buns. Turn the bowl upside-down on a lightly floured surface, and stretch the dough into a rough square shape. Pick up the right side of the dough, stretch it out, and fold it on top of the dough about halfway, like folding a letter. Repeat with the left side of the dough, and then the bottom of the dough, and finally the top. Finally, roll the dough up tightly like a towel, rolling it so that the seams are on the bottom and the smooth side is on top. Lightly flour your hands and use your fingers to tuck the sides of the dough underneath itself, so that it forms a nice round, tight ball of dough. It will be helpful to watch the video to see how to do this visually! Use a knife or a bench scraper to divide the dough into 6 pieces, weighing about 190g-200g per piece.
Working one piece at a time, gently stretch out each piece of dough into a rough rectangle. Pick up the corners and bring them into the center, pinching the corners together in the middle, to create a little packet of dough.
Flip it over so that the smooth side is facing up, and use your hands to lightly roll the dough into a tight little ball, using the counter to create tension as you shape it.Again, it will be helpful to watch the video to see how to do this visually! Repeat until all balls of dough are shaped. Place them inside of the metal rings (or spaced out on top of the baking sheet), and loosely cover with plastic wrap or a towel.
Rest the dough at room temperature for 2 hours, then transfer to the fridge to rest overnight, at least 8 hours, or up to 24 hours.