In a medium bowl, dissolve one teaspoon of the sugar (this is 1/3 tablespoon) into the lukewarm water. Sprinkle yeast on top and set aside for about 10 minutes, until frothy.
In a large bowl, combine the flour, salt and remaining tablespoon of sugar. Add the yeast mixture, melted butter, and egg, and stir until everything comes together to form a dough.
On a lightly floured surface, knead until the dough is smooth and elastic, about 5 to 10 minutes. Place dough into a lightly greased bowl, cover and let rise for 1 to 2 hours, until doubled in size.
Gently deflate the dough and divide into 8 pieces. Shape each piece into a round ball then flatten slightly and place on a lightly greased or parchment-lined baking sheet. Cover and let rise for 45 minutes to an hour, until rolls have risen and are slightly puffy. They won't quite double in size.
Towards the end of the rising time, preheat the oven to 375°F (190°C).
Brush the buns with the beaten egg and sprinkle with sesame seeds. Bake in preheated oven for 12 to 15 minutes, or until golden brown.
Transfer buns to a wire rack and allow to cool before serving.