In a large mixing bowl, combine the active sourdough starter, water, honey, and softened butter. Mix until well combined.

Add the all-purpose flour, whole wheat flour, and salt. Mix until a shaggy dough forms.

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

Place the dough in a lightly greased bowl, cover with a damp cloth, and let it rise at room temperature for about 2 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 damp cloth and let them rise for another 30-60 minutes until puffy.

Preheat the oven to 375°F (190°C).

Beat the egg and brush it over the tops of the buns. Sprinkle with sesame seeds if desired.

Bake the buns for 20 minutes or until golden brown.

Remove from the oven and let cool on a wire rack before slicing.