Prepare the Yeast Mixture: In a bowl, combine the warm water, sugar, and yeast. Let it sit for 5-10 minutes until the mixture becomes frothy.

Make the Dough: In a separate large bowl, combine the flour and salt. Pour in the yeast mixture and the cold milk. Mix until a dough forms.

Knead the Dough: Transfer the dough to a floured surface and knead for 5-7 minutes until smooth and elastic. Place it in an oiled bowl, cover with a damp towel, and let it rise in a warm spot for 1 hour, or until doubled in size.

Incorporate the Butter: Once risen, punch the dough down and transfer it to a floured surface. Roll it into a 12-inch square. Place the chilled butter cubes in the center and fold the dough over to seal the butter inside. Roll the dough into a rectangle, then fold it into thirds like a letter.

Chill the Dough: Wrap the dough in plastic wrap and refrigerate for 30 minutes. Repeat the folding and chilling process two more times (for a total of three folds). After the final fold, chill for at least 1 hour.

Shape the Croissants: Preheat the oven to 400°F (200°C). Once chilled, roll the dough into a rectangle about 1/4 inch thick. Cut it into triangles, and roll each triangle tightly from the wide end to the point.

Bake: Place the rolled croissants on a parchment-lined baking sheet. Brush them with a beaten egg for a golden finish. Bake for 15-20 minutes or until golden brown and puffed.

Cool and Serve: Allow the croissants to cool slightly before serving.