Place a fine mesh sieve over a large bowl and cover with a cheesecloth or coffee filter. Add the quark and allow to sit for a few hours to overnight in the refrigerator to drain.
Discard the liquid and place the quark in the large bowl.
In a medium bowl, sift together flour and baking powder.
Mix into the quark, then add the butter and salt until a smooth dough comes together. Cover and refrigerate for 2 hours.
Preheat oven to 400˚F (200˚C). Line a large baking sheet with parchment or lightly grease.
On a lightly floured surface, roll the dough into a rectangle just under 1/4 inch (6 millimeters) thick. Starting from the short end, fold the dough over into fourths to create four layers. Turn the dough so the new long side is now facing you. Flour lightly as needed.
Roll the dough again into a rectangle 1/4 inch (6 millimeters) thick. Fold across into fourths again and turn. Continue to repeat four more times.
Use a sharp knife to lightly score across the dough in 1/2 inch (1.25 centimeter) apart lines. Score along the other side to create a small square pattern.
Use a small circular cutter, about 1 1/2-2 inches (4-5 centimeters) across, to cut out as many rounds as close together as you can, taking care not to twist as you press down. Transfer the rounds to prepared baking sheet, 1-2 inches (2.5-5 centimeters) apart.
Gently brush the tops of the Pogácsák with the beaten egg yolk, being careful to not let it drip down the sides.
Bake in preheated oven until risen and golden brown, 20-30 minutes.