In the lukewarm milk, dissolve the sugar, then crumble in the yeast and let it stand for 10 minutes, until foamy.
In a large bowl, sift the flour, add the salt, then pour in the yeast mixture and the vanilla extract. Start kneading the dough.
Once the dough comes together, transfer it to a lightly floured surface and knead for 10-15 minutes, until elastic.
Place the dough in a large bowl, cover with a kitchen towel, and let it rise for 1.5 hours, or until doubled in size.
Roll out the risen dough into a rectangle, then place the cold butter in the center. Fold the edges of the dough over the butter.
Gently roll out the dough, then fold it into thirds. Cover and refrigerate for 45 minutes.
Repeat the folding and rolling process two more times, always resting the dough in the refrigerator for 45 minutes each time.
Roll out the finished dough to a thickness of 7 mm, then cut out a huge triangle shape.
Roll up the triangle from the wide end towards the point, to create a giant croissant shape.
Place the giant croissant on a baking sheet lined with parchment paper, cover, and let rise for another 1 hour.
Whisk the egg and brush it over the top of the croissant to give it a beautiful sheen.
Bake in a preheated oven at 350°F (180°C) for 35-40 minutes, or until golden brown and cooked through.
Let the giant croissant cool, then sprinkle with powdered sugar before serving.
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