Prepare the dough:

In a mixing bowl, combine the sourdough starter, warm milk, water, egg, butter, sugar, and salt. Gradually mix in the flour until a soft dough forms. Knead by hand for 8–10 minutes or with a stand mixer for 5–7 minutes until the dough is smooth and elastic.

First rise:

Place the dough in a lightly greased bowl, cover with a damp towel or plastic wrap, and let it rise at room temperature until doubled in size, about 4–6 hours. (Rising time may vary depending on your sourdough starter's strength and room temperature.)

Shape the buns:

Divide the dough into 8 equal portions (about 100g each if using a scale). Shape each portion into a smooth ball and flatten slightly to form a bun shape. Place the buns on a parchment-lined baking sheet, leaving space between them for expansion.

Second rise:

Cover the buns loosely with a damp towel or plastic wrap and let them rise again at room temperature for 1–2 hours, until puffed but not overly spread out.

Preheat the oven:

Preheat your oven to 375°F (190°C).

Add egg wash and toppings:

Brush the tops of the buns with the egg wash and sprinkle with sesame seeds, if desired.

Bake:

Bake the buns in the preheated oven for 18–20 minutes, or until golden brown.

Cool and serve:

Transfer the buns to a wire rack to cool completely before slicing.