Place grated zucchini in a colander, sprinkle with salt, and let sit for 30 minutes. Squeeze out excess moisture using a clean kitchen towel.
Preheat oven to 375°F (190°C).
In a large bowl, mix the zucchini with onion, green onions, dill, mint, parsley, feta, yogurt, and eggs. Season with salt and pepper.
Brush a 9x13 inch baking dish with olive oil. Layer half of the phyllo sheets, brushing each with olive oil.
Spread the zucchini filling evenly over the phyllo.
Top with remaining phyllo sheets, brushing each with olive oil. Tuck in the edges.
Score the top with a sharp knife into squares and bake for 45–50 minutes until golden brown.
Let rest for 10 minutes before slicing and serving.