Combine the flour, sourdough, egg, milk, salt, sugar, and add to the mixing machine with the hook attachment.
Mix all the ingredients for 5 minutes until the dough is sticky and cohesive.
Add the butter, then increase the speed of the mixer to a higher speed and mix the dough until it smooth and shiny.
Try the windowpane test, stretch a piece of dough until you can see through it.
Cover the dough in a bowl and let it rest in a warm place ) for about 3 hours.
Stretch and fold the dough in the bowl once after the first hour, this will degas the dough and even out the temperature of the dough.
Divide the dough into six to 6 equal pieces or weigh each piece into 100 grams.
Shape the dough pieces into tight round balls and place them on a lightly greased or parchment-lined baking sheet or into the lightly greased wells of a hamburger bun pan.
Gently flatten the dough balls about 1/2 inch them or until it comes close to filling the wells of the bun pan if you’re using it.
Cover the buns with plastic and let them rise until double the size of about 90 minutes.
Preheat the oven to 190°C or 375°F, thirty minutes before baking.
Once the buns are proofed, brush the tops with the beaten egg.
Sprinkle with topping like sesame or poppy if desired.
Bake the rolls for 18-20 minutes or until it is light golden brown.
Remove the buns from the oven. Cool it them down on a cooling rack before serving.
You can keep your sourdough hamburger buns packed in a bag for up to 5 days or freeze for up to 30 days.