In a large bowl of a mixer, combine all-purpose flour, sugar, yeast, and salt.
In a separate jug whisk together the milk and eggs.
Pour the liquid into the dry ingredients and knead on medium speed with the dough hook attachment. (Tip: hold back a little liquid in case you don't need it all to make the dough come together)
Once the dough comes together and there is no dry flour add in the sliced, softened butter. Continue to knead the dough for another 6-8 minutes. You will notice it is a soft, shaggy dough.
Turn out the dough onto a lightly floured surface and shape into a smooth ball. Place it into a greased bowl, cover the bowl with plastic wrap (or a shower cap), and keep in a warm place for 1 1/2 - 2 hours.
To make your Hamburgers: Divide the dough roughly into 6 (3 ¾oz) pieces. Shape each piece into a smooth ball and place it on a baking sheet lined with parchment paper to proof. This should take about 45 to 60 minutes. (Shaping the dough into a smooth ball is very important. Watch how, here.)
Once proofed, brush each bun with egg wash and sprinkle with sesame seeds.
Bake at 375°F (190°C) for 20-22 minutes or until they are golden brown.
Store buns in an air-tight container at room temperature for up to 2 days. Because of the butter and eggs, they can spoil after 3 days so you can either keep them in the fridge or in the freezer for longer shelf life.