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 floured surface for about 10 minutes until smooth and elastic.

Incorporate the softened butter and knead for another 5 minutes until fully combined.

Place the dough in a lightly greased bowl, cover with a damp cloth, and let it rise for about 2 hours or until doubled in size.

Once risen, punch down the dough 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 cloth and let them rise for another hour.

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 before serving.