In a large bowl, sift together the flour, baking powder, and salt.
Mix in the Túró and softened butter until a dough comes together and lightly knead on a floured surface just until smooth with no streaks of flour remaining. There may still be small pieces of cheese.
Form the dough into a disc, wrap in plastic, and refrigerate for 1 hour.
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, then wrap in the plastic and refrigerate for 30 minutes.
Remove from the refrigerator, then roll out again into a rectangle about 1/4 inch (6 millimeters) thick, flouring just as needed to prevent sticking.
Fold across into fourths again, then repeat the process one final time before wrapping in plastic and refrigerating for a final 30 minutes.
Preheat a conventional oven to 400˚F (200˚C). Line a large baking sheet with parchment or lightly grease.
Remove the dough from the refrigerator and roll into a sheet about 1/3 (8 millimeters) thick.
Use a sharp knife to very lightly score across the dough in 1/2 inch (1.25 centimeter) lines across each side to create a 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.
In a small bowl, beat together the egg yolk and water.
Gently brush the tops of the Pogácsák with the beaten egg yolk, being careful to not let it drip down the sides.
If desired, sprinkle a few sesame seeds or some grated cheese over the top.
Bake in the center of the preheated oven until puffed and golden brown, 14-20 minutes.