In a deep bowl, crumble the feta cheese into fine bits with a fork, add the eggs and stir. Add 1 tsp baking powder, pour in the warm water, stir until homogeneous.
Melt the butter and smear an 11 3/4″ (30 cm) x 8″ (20 cm) tray with 1/3 of it. Set aside 2 phyllo pastry sheets, you'll need them for the finishing touches later.
Lay out 4 sheets, 1 at a time, along the bottom and walls of the tray, such that there's sheets spilling out on all sides of the tray.
Lightly wrinkle the rest of the sheets, 1 at a time, and submerge them in the egg mixture. Next, use a fork to take them out and lay them out evenly in the tray (like a filling).
On top, place the final 2 sheets you set aside at the beginning and fold in the parts of the sheets that are spilling out. Pour the rest of the melted butter over the phyllo pastry and cut it into 4 equal-sized parts, vertically.
Separately , beat the egg very well and pour the milk into it, stir.
Pour the mixture over the phyllo pastry evenly, leave it to sit for a bit and turn the oven on to 392°F (200 °C). After it heats up, place the tray in it and bake 20 min. to a beautiful crisp.
Cover the ready phyllo pastry with a clean towel for 10 min., without sprinkling it with water. Cut the phyllo pastry, first along the cuts you made before baking, then horizontally, to make squares.
Serve warm with ayran!