I've been working on a version of this burger bun recipe for 12 years and I can confidently say that this one is IT. My PERFECT burger bun. With the use of a simple secret ingredient, this recipe reaches new levels of soft squishiness previously unknown to my home kitchen.
For accuracy, I highly recommend using measurements in grams as listed rather than volumetric (cups/tsp.)
Preheat oven to 425℉
Peel one large russet potato. Double wrap the potato in aluminum foil and roast it for 1 hour. Put the potato through a ricer and weigh it out to 150g/1 cup.
Combine all ingredients but the egg wash into the mixing bowl of a stand mixer fitted with the dough hook attachment. Mix on medium speed for 8-10 minutes. The dough will look very loose at around 4-5 minutes before it comes together into a nice ball that's no longer extremely sticky.
If you are new to making dough from scratch, I recommend watching my Youtube video linked above to familiarize yourself with the process.
Use a soaking wet hand and a grab and round dough in a 10 & 2 motion to tuck the dough into a taught ball. To do this, grab the dough at 10 o'clock and while moving your hand to the 2 o'clock postition, tuck the end underneath the dough. This will create surface tension on the dough. Repeat this process 3-4 times, until the surface of the dough is smooth and taught. Cover with a lid or plastic wrap and ferment at room temperature for 30 minutes.
After 30 minutes the dough should have gassed up quite a bit. Use your hands and fingers topress down and aggressively de-gas the dough. Once the dough has lost 50% of its volume, grab a grip of the dough and pull it up until you meat resistance and lay it into the middle. Turn the dough 180° and repeat. Repeat this with the other two sides of the dough that have not yet been folded. These are called "Strength Building Folds."
Next, flip the dough over and put the seam side down. Do another round of 10-2 and get the dough back into a nice taught ball. Cover the dough again and allow to ferment at room temperature for another 30 minutes.
It will have risen a lot again after the second ferment, so aggressively de-gas it again. Using a dough knife, divide the dough into 12 equal pieces (about 100g each).
Lightly flour your work surface and one at a time, de-gas and flatten each dough piece. Fold two sides into the dough and flip it over, seam side down. Using your hand in a circular motion, roll the dough into a taught ball on your work surface. Place the buns onto a baking sheet lined with oiled parchment. Do not overcrowd the buns. Leave it to no more than 6 per sheet tray, leaving about 3 inches between each bun. Spritz the shaped buns with water and cover with a damp towel. Proof the buns for 60-90 minutes.
Preheat oven to 400℉/205℃.
The buns are well proofed when they can take a poke and slowly bounce back. Brush top and sides of buns with egg wash (1 egg + splash water).
Load the buns into your preheated 400°F/205°C oven, spritz the oven with 10-15 sprays of water, and bake the buns for 15-18 minutes until golden brown. Be sure to rotate the buns halfway through for even browning.
Brush tops of the finished buns with melted butter.