In lukewarm milk, stir in the sugar, then crumble in the yeast. Let it stand for 10 minutes until foamy.
In a large bowl, sift the flour and add the salt. Pour in the yeast mixture and vanilla extract. Begin kneading the dough.
Once the dough comes together, place it on a lightly floured surface and knead for 10 minutes until smooth and elastic.
Place the dough in a bowl, cover with a kitchen towel, and let it rise for 1 hour, or until doubled in size.
Roll out the risen dough into a rectangle. Place the cold butter in the center of the dough. Fold the edges of the dough over the butter, enclosing it completely.
Carefully roll out the dough, then fold it into thirds. Cover and refrigerate for 30 minutes.
Repeat the folding and rolling process two more times, always chilling the dough for 30 minutes in the refrigerator between folds.
Roll out the finished dough to a thickness of about 5 mm (approximately 1/4 inch). Cut into small triangles to form mini croissants.
Roll up the triangles from the wide end towards the point to create croissant shapes.
Place the mini croissants on a baking sheet lined with parchment paper. Cover and let rise for another 30 minutes.
Whisk the egg and brush the tops of the croissants to give them a glossy finish.
Bake in a preheated oven at 375°F (190°C) for 12-15 minutes, or until golden brown.
Let the croissants cool completely, then dust with powdered sugar before serving.
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