Meanwhile, place butter between parchment paper, press, and roll into an 8x8-inch square. Chill until firm but still flexible, about 10–15 minutes.
Roll dough into a rectangle slightly wider than the butter and just over twice as long. Place butter on half, leaving a small border, then fold the other half over it. Press down with a rolling pin to create ridges, then roll out smooth. Dust with flour as needed.
Fold the dough into thirds (like a letter), press lightly, and chill for 30 minutes. Repeat rolling, folding, and chilling two more times, resting in the fridge for 15 minutes after the final fold.