1) In a small bowl, combine warm water, milk, sugar, and yeast. Let this sit for about five minutes until the yeast starts to foam.
2) In a large bowl, stir together flours and salt. Then add in soft butter and rub it into the flour, making a crumb mixture. Stir in yeast mixture next along with the beaten eggs and yolk. Stir the dough until it forms a ball. If it seems really dry, add a bit more water.
3) Scoop the dough onto a clean surface and knead the dough until it’s soft and elastic. This will probably take 8-10 minutes. If the dough is sticky at all, knead it a bit more flour.
4) Shape the kneaded dough into a ball and add it to a bowl. Cover with plastic wrap and let rise in a slightly warm place until it doubles which should take 90-120 minutes.
5) Preheat the oven to 400 degrees F and line two baking sheets with parchment paper. Divide the dough into 12 even sized balls, a little under four ounces per bun is about perfect. Gently roll each bun ball out into a flat disk and lay them a few inches apart on the two baking sheets (6 per sheet). Cover the buns with a loose, slightly damp towel, and let them rise for another hour.
6) Place a shallow pan of boiling water on the bottom of the oven to create a really humid baking environment. Beat egg with 1 tablespoon of water and brush the egg wash on the buns. THen sprinkle with sesame seeds. Bake the buns for about 15-17 minutes, rotating the pans once halfway through. The finished buns should be golden brown.
Let buns cool completely and then serve with your burger of choice!