In a large mixing bowl, combine the flour, sugar, yeast, and salt.
Add the warm water and melted butter to the dry ingredients. Mix until a dough forms.
Knead the dough on a floured surface for about 10 minutes, until smooth and elastic.
Place the dough in a greased bowl, cover, and let it rise in a warm place for about 1 hour, or until doubled in size.
Preheat the oven to 375°F (190°C).
Divide the dough into 8 equal pieces and shape each piece into a ball. Place the balls on a baking sheet lined with parchment paper.
Cover the dough balls and let them rise for another 20 minutes.
Brush the tops of the buns with the beaten egg.
Bake in the preheated oven for 12-15 minutes, or until golden brown.
Let the buns cool on a wire rack before serving.