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

Knead the dough for about 10 minutes until smooth and elastic. Incorporate the softened butter and knead for an additional 5 minutes.

Place the dough in a lightly greased bowl, cover, and let it rise at room temperature for about 2 hours or until doubled in size.

After the dough has risen, punch it down and divide it into 4 equal pieces. Shape each piece into a ball and flatten slightly.

Place the shaped buns on a baking sheet lined with parchment paper. Cover and let them rise for another hour.

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

Bake for 20 minutes or until golden brown. Remove from the oven and let cool on a wire rack.