Pour the warm milk into a large bowl and sprinkle the yeast over the surface. Let it sit for 5 minutes until the yeast blooms and becomes foamy.

Whisk together 3 and 1/2 cups flour, sugar, and salt in a separate bowl. Add the egg yolk and vanilla to the yeast mixture, then add the flour mixture and stir until shaggy dough forms.

Knead the dough for about 10 minutes until smooth and elastic, by hand or mixer. Add the 2 tablespoons softened butter partway through and knead until fully incorporated.

Place the dough in a lightly oiled bowl, cover with plastic wrap, and let it rise at room temperature for 1 to 1 and 1/2 hours until doubled in size.

While the dough rises, pound the 4 cold sticks of butter between two sheets of plastic wrap or parchment paper into a 6-inch by 8-inch rectangle about 1/2-inch thick.

Roll the chilled dough into a 10-inch by 14-inch rectangle on a floured surface. Place the butter block in the center, fold the top third down over it and the bottom third up, creating three layers (first letter fold).

Rotate the dough 90 degrees, roll gently to a 10-inch by 14-inch rectangle again, and repeat the letter fold. Repeat this process two more times for a total of four letter folds, chilling the dough 20-30 minutes between folds.

Wrap the dough tightly in plastic wrap and refrigerate for at least 8 hours or overnight to rest.

Remove dough from refrigerator and let it sit at room temperature for 10 minutes to soften slightly.

Roll to about 1/4-inch thickness, cut into desired shapes, and place on parchment-lined baking sheets with about 2 inches of space between pieces.

Cover shaped pastries loosely with plastic wrap and let proof at room temperature for 1 to 2 hours until puffy but not fully doubled.

Brush pastries with egg wash and bake at 400 degrees F for 18-22 minutes until deep golden brown.