In the lukewarm milk, stir in the sugar, then crumble in the fresh yeast. Let it sit for 10 minutes, until foamy.
In a large bowl, sift in the flour, add the salt, then rub 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 becomes smooth and elastic.
Grate the zucchini and squeeze out any excess moisture. Mix it into the dough along with the grated cheese. Cover and let it rise in a warm place for about 1 hour.
On a lightly floured surface, roll out the dough to about ¾ inch (2 cm) thickness, then fold it over itself to create layers.
Roll out the dough again to ¾ inch (2 cm) thickness, then use a round cookie cutter to cut out the scones. Place them on a baking sheet lined with parchment paper.
Brush the tops with beaten egg, then bake in a preheated oven at 350°F (180°C) until golden brown, about 20-25 minutes.
Let the scones cool on a wire rack, then serve fresh, or store in an airtight container.
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