Preheat the oven to 400 degrees . In a large pot, cook the spinach in 1 tbsp. EVOO over medium until wilted, about 3 minutes. Transfer to a colander to cool. Using your hands, squeeze out any excess liquid.
In a 10-inch ovenproof skillet, heat 1 tbsp. EVOO over medium. Add the onion and cook, stirring, until onion begins to soften, about 2 minutes. Add the zucchini and garlic and cook, stirring, until tender, about 3 minutes. Off heat, stir in the spinach, feta and dill; season with salt and pepper.
Lay the phyllo on a work surface. Brush the top sheet generously with EVOO, then place on top of the vegetables in the skillet, oiled side up, tucking in excess dough around the inside edges. Working with one sheet at a time, brush the remaining sheets generously with EVOO, then loosely crumple and place each atop one-quarter of the casserole to form a ruffled pattern.
Bake until the phyllo is golden, about 15 minutes. Slice into quarters to serve.