Peel the potatoes and cut them into smaller pieces. Make sure to weigh them after they have been peeled.
Boil them in unsalted water until very soft - this takes about 15 minutes.
Drain the water from the potatoes and put them in a bowl with the butter.
Blend them, either with a hand blender or electric whisk, until they become very sticky and "long" in consistency. Essentially the opposite of what you’ve learned about mashed potatoes.
Let the potatoes cool slightly. They shouldn't be cold, as they will be harder to incorporate into the dough. Conversely, they shouldn't still be boiling hot.
Put the dry yeast in a mixing bowl with a bit of flour, just 10-20 grams. Stir and let it sit for a few minutes. The moisture from the flour will activate the dry yeast. If you're using fresh yeast, you can simply dissolve it with the sugar, milk, and water.
Add the milk, egg, water, and sugar to the mixing bowl and stir well for 1-2 minutes.
Add the mashed potatoes and about 300 grams of the flour and mix for a couple of minutes.
Add the salt and the rest of the flour. Knead for 10 minutes, and if it doesn't seem to leave the bottom of the bowl, add a little extra flour. That’s why there’s an approximate amount of flour listed in the recipe.
Cover the mixing bowl with a lid, a tea towel, or even a shower cap and let it rise for 30-40 minutes.
Then divide the dough into 10 pieces. If you want to be precise, weigh the whole dough first and then divide into 1/10 for each. This ensures you get uniform burger buns.
Shape each piece into a tight ball by folding the dough under itself.
Place them seam-side down on a baking tray lined with parchment paper and let them rise again for about 30 minutes under a cloth.
Whisk the egg yolk with a bit of milk and brush the tops of the buns.
Sprinkle sesame seeds on top.
Bake them for about 15-16 minutes at 185 degrees Celsius (365 degrees Fahrenheit) fan-assisted - my oven is on the smaller side, so it bakes a bit faster than others.
When you take them out of the oven, there should be a hollow sound when you tap the bottom of them. If not, give them a bit more time in the oven.
Let them cool on a rack and they are ready to serve once they have cooled down.