In lukewarm milk, dissolve the sugar, then crumble in the fresh yeast. Let it stand for 10 minutes until foamy.
In a large bowl, sift the flour and add the salt. Cut in the cold butter until the mixture resembles coarse crumbs.
Pour in the proofed yeast mixture, sour cream, and whole egg. Knead the dough until it is smooth and elastic.
Mix in half of the grated Parmesan cheese into the dough. Cover and let it rise in a warm place for about 1 hour, or until doubled in size.
On a lightly floured surface, roll out the dough to about 2 cm (¾ inch) thickness. Fold the dough over itself several times to create flaky layers.
Roll out the dough again to 2 cm (¾ inch) thickness. Use a cookie cutter to cut out the pogácsa. Place them on a baking sheet lined with parchment paper.
Brush the tops with beaten egg, sprinkle with the remaining grated Parmesan cheese, and bake in a preheated oven at 180°C (350°F) until golden brown, about 20-25 minutes.
Let the pogácsa cool on a wire rack. Serve fresh, or store in an airtight container.
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