In a bowl, beat the eggs, add the finely grated feta cheese, cream, oil and carbonated water, stir very well.
Smear a tray with a little oil and lay out 1 phyllo pastry sheet along its bottom. Dip every subsequent sheet in the egg mixture, wrinkle it into a crumbly ball, dip again and arrange them next to one another in the tray. Repeat until out of mixture and you have 1 sheet left.
Place the final sheet stretched out on top, cut the phyllo pastry into squares and smear it with beaten together eggs, cream and oil.
Put the tray in a preheated 392°F (200 °C) oven, bake 40 min. total - halfway through lower the heat to 302°F (150 °C).