To begin, sprinkle the yeast over the lukewarm milk in a small bowl. Stir briefly and let it sit for about 10 minutes until it becomes frothy. In a stand mixer fitted with a dough hook or a large bowl, combine the flour, sugar, and salt. Slowly add the yeast mixture and egg into the dry ingredients, mixing until a soft dough forms. If the dough feels crumbly, add a little more milk; if too sticky, add a bit more flour. Knead the dough on a lightly floured surface until smooth and elastic, then transfer it to a large bowl. Cover and let it rise at room temperature until doubled in size, about 1 1/2 hours.

During the final 30 minutes of rising, prepare the butter layer by slicing the chilled butter into 1/2-inch (1.25 cm) thick pieces. Arrange them into an 8×8-inch (20×20 cm) square on parchment paper, cover with another parchment sheet, and pound with a rolling pin until it forms a 9×9-inch (23×23 cm) square. Refrigerate for 10 minutes until cool but pliable. Roll out the dough to an 18×10-inch (46×25 cm) rectangle and place the butter over half of the dough. Fold the dough over the butter, sealing the edges. Wrap in plastic and refrigerate for 30 minutes. Roll the dough into a 16×10-inch (41×25 cm) rectangle, fold it into thirds, and refrigerate again for 30 minutes. Repeat this rolling and folding process two more times, always chilling for 30 minutes after each fold. After the final fold, refrigerate for an additional 30 minutes.

Line two baking sheets with parchment paper. Divide the dough in half, keeping one half refrigerated while working with the other. Roll the dough into an 18×6-inch (46×15 cm) rectangle, then cut it into six triangles with a 5-inch (13 cm) base. Make a small 1-inch (2.5 cm) cut at the center of each base to help shape the crescents. Roll the triangles from base to tip, slightly turning the ends inward to form the classic crescent shape. Arrange them on the baking sheet, spacing them 2 inches (5 cm) apart. Repeat with the remaining dough. Cover lightly with a towel and let rise for 1 hour. Preheat the oven to 400°F (200°C). Whisk together the egg yolk and milk, then brush it over the pastries. Bake for 5 minutes, then reduce the temperature to 375°F (190°C) and bake for another 10-12 minutes until golden brown.