Step 1: Activate the Yeast
In a small bowl, combine the warm milk, warm water, and sugar. Sprinkle the instant yeast over the mixture and let it sit for 5-10 minutes until it becomes frothy. This step ensures the yeast is active and ready to work.

Step 2: Mix the Dough
In the bowl of a stand mixer (or a large mixing bowl), combine the flour and salt. Add the yeast mixture, egg, and softened butter. Mix on low speed until the dough comes together. Then, increase the speed to medium and knead for 8-10 minutes until the dough is smooth and elastic.

Step 3: First Proofing
Shape the dough into a ball and place it in a lightly greased bowl. Cover with plastic wrap or a clean kitchen towel and let it rise in a warm place for 1 hour or until it doubles in size.

Step 4: Shape the Buns
Once the dough has risen, punch it down to release any air bubbles. Divide the dough into 8 equal portions (about 90g each). Roll each portion into a smooth ball and place them on a parchment-lined baking sheet, spacing them about 2 inches apart.

Step 5: Second Proofing
Cover the shaped buns with a kitchen towel and let them rise for another 30 minutes. Meanwhile, preheat your oven to 375°F (190°C).

Step 6: Bake the Buns
Before baking, brush the buns with the egg wash (1 egg yolk + 1 tablespoon milk) and sprinkle with sesame seeds or poppy seeds if desired. Bake for 15-18 minutes or until the buns are golden brown.

Step 7: Cool and Serve
Remove the buns from the oven and let them cool on a wire rack. Once cooled, slice and use them for burgers, sandwiches, or any other dish!