Combine warmed 1 cup milk, 1 tbsp of the 4 tbsp white granulated sugar, and 2¼ tsp (1 pkg) active yeast together in a measuring cup. Cover and let sit warm for 10 minutes. Mixture should become frothy. If not then your yeast is dead.
While waiting for the yeast mixture to grow, mix 4¼ cup unbleached all purpose flour, 2 tsp salt, and remaining 4 tbsp white granulated sugar in a stand mixer. Make a hole in middle of the dry ingredients but not all the way through.
Drop in 4 large eggs into center of hole and pour in frothy yeast mixture.
Set mixture to low until all flour is incorporated then drop in chunks of ½ cup butter one by one. This step should take a few minutes and then remain on low for 10 minutes.
Pour out dough on a floured surface and roll into ball. Batter will be sticky. Place dough in a greased bowl and proof in a warm place for 40 minutes.
Take out dough and roll on floured surface into a log shape. Cut 12 equal sized pieces and roll each bun into a smooth bun shape and place on baking sheet.
Cover baking sheet and proof again for 30 minutes.
Beat together the yolk of 1 large egg and 1 tbsp water in a small bowl. Brush on egg wash and sprinkle on the 3 tbsp sesame seed.
Bake in a hot oven at 350°F for 25-30 minutes or until golden brown.