In a large bowl, combine flour, sugar, yeast, and salt. Add warm milk, water, and melted butter, mixing until a soft dough forms. Knead until smooth, cover, and refrigerate for 1 hour.
Place the cold butter between two sheets of parchment paper and pound into a flat 7-inch (18cm) square. Chill while the dough rests.
Roll the chilled dough into a 10×10-inch (25x25cm) square. Place the butter block in the center like a diamond, then fold the dough edges over the butter like an envelope. Seal the seams.
Roll the dough into a 20×10-inch (50x25cm) rectangle. Fold into thirds like a letter. Chill for 30 minutes. Repeat this rolling and folding process 2 more times, chilling between each turn.
After the final chill, roll the dough into a large 20×10-inch rectangle. Cut into long triangles (about 5 inches wide at the base). Roll each triangle from the base to the tip to form the classic croissant shape. Place on a lined tray with space to rise.
Let the croissants rise in a warm place for 1 to 2 hours, until puffy and slightly jiggly.
Whisk egg and milk, then gently brush over each croissant. Bake at 200°C (400°F) for 20–25 minutes, until golden brown and crisp.
Cool slightly before serving. Best enjoyed fresh and warm.
