Step 1

In the bowl of an electric mixer with the paddle attachment, mix sourdough starter, milk, 1 egg, yeast, salt, sugar and 300 grams of flour on medium speed until a loose, shaggy dough is formed.  Cover the dough with plastic wrap or a damp towel and let rest in the bowl for 30 minutes.

Step 2

With the dough hook, knead the dough for 7-8 minutes, gradually adding an additional 130 grams (or more) flour and 3 tablespoons of softened butter in small cubes.  The dough should be soft and slightly sticky, but pulling away from the edges of the bowl as it kneads.

Step 3

Pour the dough, scraping the bowl to release, onto a floured work surface.  Clean the bowl, then grease, and place the dough back into the bowl.  Cover the bowl with plastic wrap or a damp towel and place it in a warm, draft free place.  I like to keep it in the oven with the light on, but the heat off.

Step 4

After 2-3 hours, the dough should double in size.  Remove it from the bowl and place it on a floured work surface.  Divide the dough into eight equal portions (about 100 grams each).  To shape the dough into buns, pull the edges of the dough balls into the center, then cup your hand around the dough and roll into a tight ball (see video).  Place the shaped buns onto a parchment lined baking sheet a good inch apart.  Cover with a plastic wrap sprayed with nonstick spray (damp towel may stick), and let the buns rise.

Step 5

After about 1 hour and 15 minutes, the buns should be doubled in size and touching each other on the baking sheet.  Preheat the oven to 375 degrees.  Whisk 1 tablespoon of water and one egg in a small bowl, and brush onto the surface of the risen buns.  Sprinkle each bun with sesame seeds.

Step 6

Bake the buns at 375 degrees for 20-22 minutes or until deep golden brown.  The internal temperature should be about 190 degrees.  Allow to cool a bit, then transfer to a cooling rack.  Wait about 30 minutes before slicing and serving.