Let the warm water, yeast, and 2 tablespoons of sugar sit for 15 minutes.
In a bowl, add the flour, salt, and 2 tablespoons of sugar. Stir to combine.
In a separate bowl, whisk the egg and yolk. Slowly stream in the yeast mixture.
Add the softened butter and knead the dough for 10 minutes on low speed.
Lightly oil a bowl, place the dough in it, cover, and let it proof in a cold oven for 1 to 1 ½ hours until doubled in size.
Punch down the dough and divide it into 10 equal pieces. Form medium-sized buns, gently flattening them.
Let the buns proof for 45 to 60 minutes until doubled in size.
Brush the buns with egg wash and sprinkle with roasted sesame seeds.
Bake at 375°F for 12 to 14 minutes.
