Cut the filo or lavash into wide strips.
Whisk eggs, milk, sparkling water, and salt in a bowl.
Grease a baking dish very well with butter or oil.
Layer half of the dough in the dish.
Pour half of the egg mixture evenly over the dough.
Spread feta and mozzarella evenly on top.
Add the remaining dough.
Pour the rest of the egg mixture evenly over the top.
Bake at 180°C (350°F) for 35–40 minutes, until golden.
For extra crispiness, carefully flip the börek and bake a few more minutes.
Let rest slightly, slice, and serve warm.