Preheat your oven to 350°F (175°C). Grease a 9x13 inch (23x33 cm) baking dish with vegetable oil.
In a large bowl, whisk together the eggs, whole milk, plain yogurt, vegetable oil, salt, and baking powder until well combined.
Stir in the crumbled feta cheese and cottage cheese. Mix until fully incorporated.
Place one sheet of phyllo dough in the greased baking dish, allowing the edges to hang over the sides.
Brush the phyllo sheet lightly with the egg mixture.
Repeat this process, layering and brushing each sheet with the egg mixture until you have used about half of the phyllo dough.
Pour the cheese mixture evenly over the layered phyllo dough.
Continue layering the remaining phyllo sheets on top of the cheese mixture, brushing each sheet with the egg mixture.
Once all the phyllo sheets are layered, fold the overhanging edges over the top to seal the gibanica.
If using, pour the sparkling water evenly over the top layer. This will make the gibanica extra fluffy.
Bake in the preheated oven for 45-50 minutes, or until the top is golden brown and the filling is set.
Allow the gibanica to cool slightly before cutting into squares.
Enjoy your meal!