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In the bowl of a stand mixer fitted with the dough hook, combine the milk, water, yeast, sugar, and egg. If using active dry yeast, let the mixture sit for 5 minutes, until frothy, before continuing. Add the flour to the bowl, and mix until incorporated. Mix in the salt and butter. Knead on medium low speed for about 10 minutes, or until the dough comes together into a soft yet tacky dough (should not be unbearably sticky). Avoid adding too much extra flour because it will create tough buns, it’s better to be sticky than dense I promise!
Transfer the dough to a lightly oiled bowl. Cover with plastic wrap and let rise in a warm place until doubled in size, about 1 to 2 hours.
Line two baking sheets with parchment paper or silicone baking mats. Divide the dough into 8 equal parts. Gently roll each portion of dough into a ball and place on baking sheet, 2 to 3 inches apart. Cover with a clean towel and let rise again until puffy and almost doubled, 1 to 1 1/2 hours.
Preheat the oven to 400°F. Brush the tops of the buns lightly with the egg wash. Sprinkle with sesame seeds. Bake the buns about 15 minutes, rotating halfway through baking, until the tops are golden brown. Transfer to a rack to cool completely. Serve or store in an airtight container in the freezer for up to one month. Let defrost at room temperature before reheating in a 350°F oven until warmed or toasting.