In lukewarm milk, dissolve the sugar, then crumble in the yeast. Let it sit for 10 minutes, until foamy.
In a large bowl, sift in the flour and add the salt. Cut in the cold butter until the mixture resembles coarse crumbs.
Pour in the proofed yeast, sour cream, and whole egg. Knead the dough until it is smooth and comes together.
Cover the dough and let it rise in a warm place for about 1 hour.
Meanwhile, clean and finely chop the mushrooms. Heat the oil in a skillet, add the minced garlic, then the mushrooms. Sauté until softened, then let it cool completely.
On a floured surface, roll out the risen dough to a thickness of approximately ¾ inch (2 cm). Evenly spread the cooled mushroom mixture and grated cheese over the dough, then fold the dough over itself.
Roll out the dough again to a thickness of ¾ inch (2 cm). 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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