In a large bowl, whisk together flour, sugar, yeast, and salt. Cut 2 tablespoons of butter into small pieces and add to the flour mixture. Pour in cold milk and stir until a shaggy dough forms. Turn out onto a lightly floured surface and knead for 3-4 minutes until smooth. Wrap in plastic and refrigerate for 1 hour.

Place remaining 1 1/4 cups cold butter between two sheets of parchment paper. Pound with a rolling pin, then roll into a 7x10-inch rectangle. Refrigerate the butter block for 20 minutes while the dough chills.

On a floured surface, roll the chilled dough into a 10x16-inch rectangle. Place the cold butter block in the center and fold the dough over it like a letter, encasing the butter completely. Pinch the seams to seal.

Roll the dough into a 10x20-inch rectangle, working from the center outward. Fold the bottom third up and the top third down (like a letter). Wrap in plastic and refrigerate for 30 minutes. This is your first fold.

Repeat the rolling and folding process two more times, chilling for 30 minutes between each fold. After the third fold, wrap the dough tightly and refrigerate overnight (or at least 4 hours).

Roll the chilled dough into a 12x30-inch rectangle about 1/4-inch thick. Using a pizza cutter or sharp knife, cut into long triangles with a 4-inch base. Make a small notch at the base of each triangle, then roll from the wide end to the point, stretching gently as you roll.

Place shaped croissants on parchment-lined baking sheets, seam side down, spacing them 3 inches apart. Curve the ends slightly inward to form a crescent. Cover loosely with plastic wrap and let proof at room temperature until nearly doubled and jiggly when shaken, 2-3 hours.

Preheat oven to 400°F (200°C). Place a shallow pan of boiling water on the bottom oven rack. Brush proofed croissants gently with egg wash, covering all surfaces. Bake for 18-22 minutes, rotating the pans halfway through, until deep golden brown. Cool on a wire rack for 10 minutes before serving.