In a stand mixer with a dough hook, add sourdough starter, warm water, all purpose flour, melted butter or coconut oil, honey, salt and egg.

Knead for 5-10 minutes with dough hook until smooth and elastic. (Note: Full 10 minutes is often required for high-fat/egg doughs to develop the necessary gluten matrix.) You will notice the dough transition from a shaggy, breaking mass to a smooth, shiny ball that clears the sides of the bowl.

Place dough in a greased bowl and cover with a damp towel or plastic wrap for 8 hours for bulk fermentation.

Transfer the dough to the refrigerator and chill covered overnight. This step is non-negotiable for proper structure and flavor development.

Divide the cold dough into eight equal pieces using a digital scale for consistency.

Shape the buns by gently flattening the dough into a small disc, folding the edges toward the center to create a pouch.

Flip the dough over so the seam side is down.

Using the edge of your hand and the friction of the counter, rotate the ball in a circular motion to create surface tension (the critical 'tucking' step). Use the damp hand technique if the dough becomes too sticky, avoiding excess flour.

Cover the shaped buns with plastic wrap or a damp tea towel and allow to rise until doubled in size (2 to 4 hours).

Preheat oven to 350 degrees F.

Beat the egg yolk and water together and brush the tops of the buns with the mixture.

Sprinkle with sesame seeds, if using.

Bake the buns for 20 minutes, or until golden on top. (Note: The schema specifies 20 minutes cook time, while the text states 25-30 minutes; using the shorter time derived from the schema's PT20M). Place a shallow pan of water on the bottom rack for the first ten minutes for a softer crust, if desired.

Immediately transfer the finished buns to a wire cooling rack.