Combine all-purpose flour, salt, and egg in a large mixing bowl, and pour the yeast mixture. Mix well with a spatula. Using a stand mixer with a dough hook, knead the dough for 5 minutes at high speed until smooth.
Add softened butter, and continue kneading for 5 minutes at medium-high speed until the butter has completely absorbed and the dough becomes smooth and more elastic. (If kneading by hand, you should spend less than 10 minutes to get a smooth dough.)
Preheat the oven to 356°F (180°C). Brush the buns with melted butter and bake for 15 minutes or until golden brown. Transfer them to a cooling rack and brush more melted butter on top while still warm.