Warm the Greek yogurt in the microwave for about 30 seconds, just enough to take the chill off and bring it closer to room temperature. Then mix to combine. You want it slightly warm but not hot. If the yogurt is too hot it can kill your sourdough starter when you mix them together.
In the bowl of a stand mixer fitted with the dough hook, combine the sourdough starter, warmed Greek yogurt, egg, and sugar. Mix on low until combined.
In a separate bowl, whisk together the bread flour, baking powder, and salt. Pour the dry ingredients on top of the wet mixture. Cut the butter into roughly marble sized pieces and add them to the bowl.
Mix on low speed until a shaggy dough begins to form, and then flour is all incorporated.
Cover and let rest 30 minutes. Yogurt hydrates the dough differently than just water or milk.
Mix on low speed until a shaggy dough begins to form, and then flour is all inoorporated. then increase to medium low and knead for 4 to 5 minutes until the dough is soft, smooth, and slightly tacky.
If the dough feels too sticky, and isn't pulling away from the sides of the bowl, add flour 10 to 15 grams at a time. Different yogurt brands and humidity levels will affect how much flour you need.
For hand mixing: In a large bowl, whisk the sourdough starter, warmed Greek yogurt, egg, and sugar until combined. In a separate bowl, whisk together the bread flour, baking powder, and salt. Pour the dry ingredients on top of the wet mixture and cut the butter into marble sized pieces over the bowl. Using your fingers, pinch the butter into the flour until it is worked through. Then slowly start mixing the flour and wet ingredients together until a dough forms. Turn out onto a lightly floured surface and knead by hand for 5 to 6 minutes until smooth and soft. Lightly flour your hands and surface as needed if the dough gets sticky.
Shape the dough into a ball, place it back in the bowl, and cover with a damp towel or plastic wrap. Let it rest at room temperature for 1 hour.
After 1 hour, perform one set of stretch and folds. With wet or lightly oiled hands, grab one side of the dough, stretch it up, and fold it over the center. Rotate the bowl and repeat three more times until you have folded all four sides. Flip the dough seam side down, cover, and let it continue to rise at room temperature until the dough has noticeably puffed up and feels light and airy when you gently shake the bowl, about 5 more hours (approximately 6 hours total from mixing). The timing will vary depending on your kitchen temperature. A warmer kitchen will be faster, a cooler kitchen will take longer. Do not rush this step. Enriched doughs with butter, egg, and sugar take longer to rise than lean doughs.
Once the dough has risen, turn it out onto a lightly floured surface and weigh it. Divide into 12 equal pieces using a bench scraper. If you want to be accurate each dough ball will weigh about 58 grams.
Roll each piece into a tight ball by tucking the edges underneath and creating surface tension. Place them on the counter and push and pull in a circular manner to create a taunt dough ball. Place them in a parchment lined 9x13 baking pan so they are just touching.
Cover the pan and let the rolls proof for about 2 hours until puffy. If your house runs cool, place the pan in the oven with just the light on for the last hour to give them a gentle push.
Remove the rolls from the oven if proofing inside and preheat the oven to 375 degrees F.
Whisk together the egg white and a splash of water to make the egg wash. Brush each roll generously with the egg wash and sprinkle with flaky sea salt if desired.
Bake for 20 to 25 minutes or until the rolls are lightly golden on top.
Remove from the oven and brush the tops immediately with melted butter. Let cool for 10 to 15 minutes before serving.