In a large mixing bowl, combine the sourdough starter, flours, sugar, salt, milk, and softened butter. Mix until a shaggy dough forms, then knead (by hand or mixer) until smooth and slightly tacky, about 6–8 minutes. Add small amounts of water, as needed, for hydration.
Cover the dough and let it bulk-ferment at room temperature (ideally 70–75°F) for 4–6 hours, performing 2–3 sets of stretch and folds during the first 2 hours.
Once the dough has nearly doubled and feels puffy and airy, turn it out onto a lightly floured surface. Divide into 8 equal portions and gently shape each into a tight round. A digital scale helps keep each round similar (around 130-ish grams).
Place the shaped buns on a parchment-lined baking sheet, spaced evenly apart. Lightly flatten the tops with your palm. Cover loosely and proof at room temp for 2–3 hours, or until they’ve puffed and airy looking. (Watch the dough versus going by the time. The dough and room temperature play an important part in how long this will take.)
Preheat the oven to 375°F (190°C). Brush each bun with egg wash and sprinkle with sesame seeds, if using.
Bake for 20-25 minutes, or until golden brown and hollow-sounding when tapped on the bottom. If you have an instant digital thermometer, look for 190-200º F. Cool completely before slicing.