In a mixing bowl, combine 220 grams of warm milk and 40 grams of granulated sugar, stirring until the sugar dissolves. Next, gently fold in 150 grams of sourdough discard and 1 teaspoon of instant yeast, creating a smooth mixture. Let it sit for about 5 minutes until the yeast begins to foam.

Incorporate 420 grams of unbleached bread flour into your wet mixture, stirring with a wooden spoon until a shaggy dough begins to form. Transfer to a lightly floured surface and knead for about 8-10 minutes until smooth and elastic.

Gradually knead in 2 tablespoons of softened butter and 1 teaspoon of salt for about 5 minutes until fully incorporated; the dough should feel soft and slightly tacky.

Place your kneaded dough in a greased bowl, cover with a damp kitchen towel, and set in a warm area to rise until nearly doubled in size, about 1-2 hours.

Transfer the dough onto a floured surface and divide it into 8 equal portions, shaping into smooth balls. Let them rest for about 30 minutes, covered with a kitchen towel.

Take each rested dough ball, gently flatten it, and roll into a log approximately 7 inches long. Place the shaped logs onto a parchment-lined baking sheet.

Cover shaped buns loosely with a kitchen towel and let them rise again until doubled in size, about 45 minutes. Preheat your oven to 375°F (190°C).

Beat 1 tablespoon of egg white or a substitute for glazing. Gently brush the tops of the risen buns with this egg wash just before baking.

Bake the buns in the preheated oven for approximately 25 minutes until they turn a rich, golden-brown color.

Brush the freshly baked buns with 2 tablespoons of melted butter immediately once out of the oven. Let them cool on the baking sheet for a few minutes.

After cooling slightly, slice the buns along the top, creating a pocket for your favorite fillings.