In a glass measuring cup, combine the warm water, milk, sugar, and yeast. Allow the yeast to proof (get all foamy and bubbly) for 5-10 minutes. Meanwhile, in a separate bowl, gently beat 1 egg and the yolk of the second egg, reserving the white of the second egg for brushing the tops of the buns before baking them.

Add the yeast and beaten egg and yolk to the flour mixture. Mix on medium-low speed with your paddle attachment for 5-8 minutes, until a very sticky and wet dough forms.

Cover the bowl with plastic wrap and let the dough rise in a warm place until doubled in size, roughly 1-2 hours. Meanwhile, line a baking sheet with parchment paper.

Once the dough has risen, punch it down and turn it onto a lightly floured surface and divide it into 8 equal-size parts using a bench scraper or pizza cutter.

Shape each portion of dough into a smooth ball by flattening it slightly and then tucking the edges together at the back to create a seam. Gently roll into a smooth ball and then set the ball of dough down on your parchment-lined pan so that the seam is on the bottom and there is a smooth, domed top to each bun. Space the buns 2-3 inches apart to allow for expansion.

Loosely cover the shaped buns with plastic wrap and allow to rise for another 1-2 hours, then beat the reserved egg white from earlier with a splash of water and use it to gently brush the top of each bun with egg wash so that it will brown nicely and have a beautiful shine when baked. Sprinkle with sesame seeds, if desired.

Preheat oven to 400 degrees. Just before putting the buns in the oven, place a pan with a cup of water on the bottom rack of the oven to create steam while the buns bake. Place the buns in the oven on the rack above the water and bake for 15-20 minutes, or until golden brown. Cool completely before slicing in half and serving.