How to Make Hamburger Buns:
Firstly, mix the water, yeast and 100 g of the flour into the mixer bowl and carefully whisk by hand to combine.
Let the mixture stand for 15 minutes, after which time it should become foamy, and its volume increase, as shown in the picture below.
Into this batter, add the egg, the melted butter, sugar, and salt, and whisk gently to combine.
Then add the remaining 350 grams of flour, and mix roughly with a silicone spatula.
Put the bowl onto the mixer and attach the dough hook. Set the speed to low and knead for about 15 minutes. The dough will become very soft and flexible. Check the kneading process often, stopping the machine to scrape dough from the sides of the bowl back into the middle for even kneading.
After kneading comes the proving stage. Take a large bowl and brush the inside with grape seed oil (or other oil light in color and taste such as vegetable or peanut oil).
Take the dough out of the mixer. If it is very sticky, rub a little grape seed oil over your hands and mold it into a smooth ball. Put the dough into the greased bowl and fold it over a few times so that it is coated with a thin layer of oil, placing the ball folded side down. Cover with plastic wrap.
Allow the dough to prove at room temperature (23-25 degrees Celsius) for 2 hours. Do not try to speed up the proving process by setting the dough in a higher temperature environment, or you risk over-proving the dough or killing the yeast. The ambient temperature and yeast activity will differ, so 2 hours is only approximate. The dough is ready when it has doubled in size, as shown below.
The third step is shaping the dough into buns. Divide the dough into eight equal portions. The best way to get them even is to weigh the dough, then keep cutting it in half until you have eight pieces. Weigh each portion so it equals 1/8 of the total.
Lay a sheet of baking paper onto a chopping board and place the dough portions on the paper, so they won’t stick to the chopping board. Gently knead and smooth each portion for about 2 minutes to remove any big bubbles.
Fold the edge of the dough to the center, so it gradually becomes a flat and spherical to a diameter of 7 cm.
Line a deep baking pan with a layer of baking paper and arrange the buns, creased side down, about 3 cm apart, so they will not stick together during the second proving.
Finally, sprinkle each bun with a little flour, cover the baking pan with a damp cloth and let it stand at room temperature for 1 hour.
While you are waiting for the dough to prove, preheat the oven to 190 degrees Celsius.
Put the rest of the eggs in a small bowl, add the milk, and whisk together until the mixture is nice and uniform with no lumps of egg.
After the buns have proved, brush them with the egg glaze. An egg glaze is what gives the buns their beautiful golden-brown tops. Not glazing the buns will produce a very pale color, no matter how long you cook them.
Top the buns with a sprinkling of sesame seeds and pop them into the oven to bake for 15-17 minutes until the tops are light brown. Because the temperature of each oven is different, keep an eye on those buns from the 13-minute mark and once the bread color is right, take them out of the oven and immediately place on a cooling rack.
Ok, the bread is done, so now we can get into the meaty stuff of making burgers!