In a mixing bowl, combine the bread flour, sourdough starter, water, salt, and sugar. Mix until a shaggy dough forms.

Knead the dough on a lightly floured surface for about 10 minutes until smooth and elastic.

Incorporate the softened butter and knead until fully integrated.

Place the dough in a lightly greased bowl, cover, and let it rise at room temperature for 4-6 hours or until doubled in size.

Once the dough has risen, punch it down and divide it into 4 equal pieces.

Shape each piece into a round bun and place them on a baking sheet lined with parchment paper.

Cover the buns with a kitchen towel and let them rise for another 1-2 hours until puffy.

Preheat the oven to 375°F (190°C). Brush the tops of the buns with the beaten egg and sprinkle with sesame seeds if desired.

Bake for 20 minutes or until golden brown. Let cool on a wire rack before serving.