In a large bowl of the stand mixer, attach the hook attachment. Add in the large bowl all-purpose flour, sugar, salt and dry yeast. Stir with wooden spatula to combine these dry ingredients.
Heat the milk to lukewarm temperature and add it to the bowl with the flour mixture. Start mixing on speed 1 (stir) and slowly increase the speed 2-3. When you see the dough slowly comes together, add the softened unsalted butter.
Continue mixing the dough for about 10 minutes, or until the dough comes well together, and it's not sticking to the sides of the bowl anymore. The dough might still be lightly sticky to the touch. If your dough is visibly too sticky, add a teaspoon of flour and continue mixing until it's not sticking to the bowl. If the dough isn't coming together, add a small teaspoon of softened butter or canola oil.
Place the dough on a floured surface and gently shape it into the bowl. Place it back to the bowl and cover with plastic food foil or clean kitchen towel. Let the dough prove in a warm (non drafted) place for 1 hour or until it doubles in size.
Remove the bun dough from the bowl and place it on a floured working surface. Cut the dough in 8 equal pieces. Start shaping the bun by tucking the corners of the dough inside. Once the dough has a shape of a bun, turn it upside down, with the soft side up. With both hands turn gently the bun (on the working surface) in your hands by lightly pressing on sides and reshape the bun more in ball shape. Place the buns on a baking sheet covered with parchment paper.
Prepare egg wash by cracking the egg in a small ceramic bowl or cup and whisk it with a fork. Brush the egg wash over the buns, sides also and cover them with plastic food wrap or clean kitchen towel. Let the buns prove for a second time, for 20 minutes.
In the meanwhile reheat the oven to 200 C / 395 F. Once the buns have doubled in size, brush them again with remaining egg wash and sprinkle with sesame seeds.
The buns are ready to be baked. Place a roasting pan with 1 cup of lukewarm water on the bottom rack, to create the steam. On the middle rack, place the baking sheet with the buns. Bake the buns for 15 minutes. After 15 minutes remove the roasting pan with water and continue baking the burger buns for an additional 10 minutes.
After the baking, either place the buns on a baking rack to cool them off quickly. Or you can leave them on the baking sheet to cool them off directly on the baking sheet.