In a large bowl, combine the warm milk, yeast, and sugar. Let it sit for about 5-10 minutes until foamy.
Whisk in the eggs and melted butter.
In a separate bowl, whisk together the flour and salt. Gradually add the dry ingredients to the wet ingredients, mixing until a shaggy dough forms.
Turn the dough out onto a lightly floured surface and knead for 8-10 minutes, or until smooth and elastic. Alternatively, use a stand mixer with a dough hook.
Place the dough in a lightly oiled bowl, cover with plastic wrap, and let it rise in a warm place for 1-1.5 hours, or until doubled in size.
Punch down the dough and divide it into 8 equal portions. Shape each portion into a ball and flatten slightly.
Place the dough balls on a baking sheet lined with parchment paper, leaving some space between them. Cover and let them rise for another 30-45 minutes.
Preheat your oven to 375°F (190°C).
Whisk together the egg and water for the egg wash. Brush the tops of the buns with the egg wash. Sprinkle with sesame seeds if desired.
Bake for 15-20 minutes, or until golden brown and cooked through.
Let the buns cool on a wire rack before slicing and serving.
Notes
Store leftover buns in an airtight container at room temperature for up to 3 days.