Hydrate and Rest the Dough
Whisk the egg, lukewarm water, milk, and 1 tsp salt together in a small bowl. Place the flour in a large mixing bowl, create a well in the center, and pour in the liquids. Stir with a fork until a shaggy dough forms, then turn it out onto a clean counter. Knead by hand for 8-10 minutes until smooth and elastic. Wrap tightly in plastic wrap and leave at room temperature.
Kneading develops the essential gluten framework, while the long rest relaxes those bonds so you can roll the dough paper-thin without it springing back.
The dough transforms from a shaggy, bumpy ball to a silky, satin-smooth surface. When pressed with a finger, the dent slowly recovers.