In the lukewarm milk, stir in the sugar and crumble in the yeast. Let it stand for 10 minutes, or until foamy.
In a large bowl, sift the flour, add the salt, then rub in the cold butter until the mixture resembles breadcrumbs.
Pour in the foamy yeast mixture, sour cream, and whole egg. Knead the dough until it is smooth and elastic.
Finely chop the fresh basil and mix it into the dough along with the grated cheese. Cover and let rise in a warm place for about 1 hour.
On a lightly floured surface, roll out the dough to about 2 cm (¾ inch) thickness, then fold it over itself several times to create layers.
Roll out the dough again to 2 cm (¾ inch) thickness, then use a round 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 180°C (350°F) 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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