In a large bowl, combine the active sourdough starter with warm water. Stir in the bread flour, salt, and sugar until a rough dough forms. Add the softened butter and mix thoroughly until the dough is smooth and elastic (about 8-10 minutes of kneading by hand or 5-6 minutes with a stand mixer).

Cover the bowl with a kitchen towel or plastic wrap. Let the dough rise at room temperature until it has roughly doubled in size. This usually takes about 3-4 hours, depending on the temperature and starter activity.

Once risen, turn the dough out onto a lightly floured surface. Divide it into 8 equal portions. Shape each piece into an elongated bun shape (about the length of a hot dog). Place the buns on a parchment-lined baking tray, leaving some space between them for expansion.

Cover the shaped buns loosely and allow them to proof for another 1-1.5 hours until puffy and nearly doubled.

Preheat your oven to 375°F (190°C). Beat the egg lightly and brush it gently over the tops of the buns for a shiny, golden crust.

Bake the buns for 18-20 minutes, or until they are golden brown and sound hollow when tapped on the bottom. Remove from the oven and transfer to a wire rack to cool completely before slicing and serving.