In a large bowl, whisk flour, sugar, salt, and instant yeast together, avoiding contact of the yeast with salt until mixed.

Pour cold water and cold milk into the dry mixture. Add the 3 Tbsp softened butter and stir until a rough dough forms.

Turn the dough onto a clean surface, shape it into a rough rectangle, wrap in plastic wrap, and chill in the fridge for 30 minutes to 1 hour.

If dough is too sticky after chilling, give a few gentle folds on a lightly floured board.

Prepare the butter block by placing the 1¼ cups cold unsalted butter between two sheets of parchment paper, pound and roll it to form a flat square about 8 inches. Chill if it softens.

On a floured surface, roll the chilled dough into a rectangle large enough to enclose the butter block. Place the butter block on one half of the dough and fold the other half over it. Seal the edges.

Roll the dough into a long rectangle and then fold it into thirds like a letter. Wrap and chill for 30 to 45 minutes.

Repeat the rolling and folding process two more times, chilling for 30 to 45 minutes each time, and ensure the dough rests for at least 1 hour or overnight for cleaner layers.

Roll the chilled dough into a 20 by 12-inch rectangle and about 1/8 inch thick. Trim the edges for straight sides.

Using a sharp knife and ruler, cut the dough into long triangles, aiming for a base width of 4 to 5 inches per croissant.

Make a small slit at the base of each triangle, roll from the base to tip while stretching a little, curve the ends if desired, and place on parchment-lined baking sheets.

Beat the egg with a pinch of salt and brush lightly over each croissant for a glossy top.

Let the croissants proof at room temperature until puffy and nearly doubled in size, which can take 1 to 2 hours.

Preheat oven to 400°F (200°C).

Bake the croissants for 12 to 18 minutes until deep golden brown and crisp, rotating sheets if necessary.

Remove from oven and let cool on a rack for 10 minutes before serving.