In a bowl, combine flour, sourdough discard starter, cold water, salt, and softened butter. Mix until a rough dough forms. The dough should feel firm but not dry.
Shape into a rectangle, wrap, and place in the fridge for at least 2 hours or overnight. Resting time allows the flour to hydrate and makes rolling easier.
Place the cold butter between two sheets of parchment paper and gently roll it into a flat rectangle about half the size of your dough. I prefer to hammer it out first with the rolling pin. This makes it much easier to roll.
The butter should be cold but pliable while rolling. If it becomes too soft at any point, return it to the fridge for several minutes until firm again.
Roll the chilled dough into a rectangle large enough to fully enclose the butter block.
Place the butter in the center of the dough. Fold each corner of the dough over the butter toward the center, overlapping slightly and sealing the edges so the butter is completely enclosed.
On a floured surface, roll the dough gently into a long rectangle.
Fold the bottom third up and the top third down, like a letter.
Wrap and chill in the fridge for 30 to 45 minutes. Repeat the rolling and folding process two more times, chilling between each fold. These folds create the flaky layers that define puff pastry.
After the final fold, chill the dough for at least 2 hour before using. The pastry is now ready for recipes or can be stored in the fridge for up to two days, or frozen for up to 2 months.