Take the butter and eggs out of the fridge and let them come up to room temperature.
In the bowl of your stand mixer, combine eggs, sugar, milk, and yeast and whisk them together.
With the dough hook attached, start the mixer on medium speed.
Add the salt and then add the flour little by little. Scrape down the sides of the bowl as needed.
When all the flour has been combined, start adding the butter little by little. Wait for it to be incorporated before adding more.
Keep mixing until the dough clears the sides (but not necessarily the bottom). Somewhere around 20-25 minutes.
Spray a container with nonstick spray and move the dough to the container. Cover it with cling film and put it in the fridge to retard for at least 2 hours. You can leave it in the refrigerator until the next day.
When you are ready to shape your buns get the dough from the fridge.
Put the molds on a baking sheet.
Measure out 90 grams (about 3 oz) of dough per bun (this fits my 10.5 cm/4 ⅛ inch mold).
Shape the bun pushing the side of the dough underneath the dough ball, turn it a little bit, and keep going to create a taut side on top.
Once the bun has an excellent surface tension, put it down on your unfloured kitchen counter and put your hand over the ball like a claw. The palm of your hand should be touching the ball lightly.
Move your hand in circles until you have a completely round ball.
Put it in the middle of your mold and cover it with a dishtowel.
Repeat with the remaining dough. It should make eight buns with maybe a little leftover.
Spray the buns lightly with oil and press them flat with your hand.
Cover with a dish towel and leave to proof somewhere warm until doubled, for about two hours.
Before the two hours are up, preheat your oven to 175°C/375°F/Gas Mark 4. Do not use fan assist.
Add a pan of boiling water to the bottom of your oven.
Prepare an egg wash combining the remaining egg and remaining milk.
Brush the buns with the egg wash.
Sprinkle with seeds if you want. For me, a burger bun needs toasty sesame seeds.
Add the pan to the oven and spray the sides of the oven with water.
Bake for five minutes. Remove the steaming pan and bake for another five minutes.
Check the internal temperature. It should be 96°C/205°F. Keep baking until it hits the right temperature.
Let the buns cool on a wire rack. They can be stored in a plastic bag, which will help the crust become soft. Store in the freezer for up to three months.