Combine water, sugar, and yeast in a small mixing bowl. Set aside for 5-10 minutes to activate the yeast.
In a separate medium sized bowl, combine the sourdough discard, melted butter, egg, and salt.
Add the activated yeast to the medium sized bowl and mix.
Gradually add the flour and mix together. Feel free to add more flour if needed to decrease the stickiness of the dough.
Knead the dough for 8-10 minutes until smooth and elastic on a floured surface.
Place dough in a greased bowl, cover, and place in a warm spot for 1-2 hours until doubled in size.
After the dough has doubled in size, punch the dough to release the air.
Divide the dough in 8 equal portions (mine is usually around 100 grams each).
Shape each dough in a round ball and flatten the top to form a bun. *See notes below Place buns on a pan lined with parchment paper and cover for 30-45 minutes to complete the second rise.
Preheat oven to 375°F.
After the buns have risen, brush the tops with milk to create a golden brown color while baking. **See notes below Bake the buns for 15-20 minutes at 375°F until golden brown on top and you hear a hollow sound inside when you tap the bottom of the buns.
Allow buns to cool before cutting them in half horizontally to create a top and bottom bun.