In the bowl of a stand mixer mix the warm water (380g) and yeast (7g). If using instant yeast, proceed. If using non-instant, add a pinch of the sugar, wait 10-15 minutes until bubbly.
Add the sourdough starter (200g) and mix.
Add the egg (1), melted butter (55g), and mix.
Reserve 50g of the flour.
Add about half the flour (780g) of the flour, the salt, and the sugar. Mix on low until combined and then add the rest of the 780g flour.
Mix on low until combined, then mix on medium for 7-8 minutes. If the dough is too sticky, add a bit of the reserved flour.
Spray with oil, turn to coat, cover and let rest for 60-90 minutes until just about doubled but definitely very puffy.
Put parchment on a sheet pan. (Two if you don't want the buns crowded and baking together.)
Punch the dough down on a lightly floured surface and divide into 12 pieces -- should be 125-130 grams each.
Roll into a ball and then press flatter and put onto the parchment-lined baking sheet (12 on one sheet or 6 per sheet on two sheets).
Cover with a towel and let rise for 45-60 minutes until, again, puffy.
Preheat oven to 425℉ standard or 400℉-Convection.
While oven is heating, mix egg with a tablespoon of water and brush the tops with this egg mixture.
If desired, sprinkle with sesame seeds (white or black), nigella seeds, or a combination of the two.
Bake for 15-18 minutes until golden brown and a thermometer registers 190℉ in the middle. (You know your oven -- you may need to switch pans around, rotate, etc. mid-bake as you know happens in your oven.)
Remove from oven and remove to a cooling rack. Let cool an hour or more before serving.