Grate the zucchini and potatoes coarsely. Put them into a colander and press them with your palm to drain out their juice as much as possible. The carrots are also grated. The onions and garlic are chopped finely. In a pot, heat half the olive oil.
Sauté the onions and garlic for 4-5 minutes. Add the carrots and mix thoroughly. Add the drained zucchini and potatoes, and herbs. Leave it to stew for another 5-6 minutes, stirring occasionally. Remove from the heat and leave it to cool to the side.
On top of the vegetables, crumble the feta cheese and add the beaten eggs. Sprinkle the filling with salt and black pepper. Heat the oven to 392°F (200 °C).
Coat a suitable tray with a little olive oil. On the bottom, arrange half of the phyllo pastry sheets, coat them with a little olive oil in between. Distribute the stuffing. Put the other sheets on top. Smear the pie with olive oil and cut it into pieces.
Bake for about 30 minutes in a pre-heated oven. Once removed, allow it to cool slightly.