In a stand mixer* with a dough hook, combine warm water, milk, yeast and sugar. If you are using active dry yeast, wait for about 6-10 minutes for the yeast to get foamy. If you are using instant yeast, you can immediately proceed to next steps.
Add bread flour and mix together. With the mixer still on, add softened butter in chunks, an egg and additional egg yolk, and salt. Add all purpose flour until the dough is soft and elastic. Elevation, how you measure, and brand of flour can impact the amount needed. You may need a little less or more.
Knead for 8 minutes.
Transfer to a large greased bowl, cover, and let rise until doubled - 30-60 minutes. (You can also stick this straight in the fridge and let it slow rise in the fridge overnight.)
Once the dough has doubled, punch it down to release the gas bubbles. Transfer to a floured work surface and divide into 8 even sections. Form into a circle and tuck all the ends in to form a ball. Then flip it over so the seam is facing down on the counter and roll the ball in circular motion to seal the bottom seams and tighten the shaped ball.
Repeat this process for the remaining sections. Place shaped buns onto a parchment lined baking sheet, keeping them spaced at least two inches apart (4-6 will fit well on a pan).
Loosely cover the buns and let them rise until almost doubled in size, about 30-45 minutes (depending on how warm your home is). Meanwhile, preheat your oven to 400° F.
Prepare an egg wash by whisking together 1 egg and about 1 tbsp of water. Just prior to placing risen buns in the oven, brush them with egg wash. Top with sesame seeds if desired.
Bake for 16-18 minutes, until tops and bottoms are a deep golden brown. Brush with melted butter if desired. Cool completely and then slice before serving.