Place a large skillet over medium heat. Add 2 tablespoons of olive oil and the chopped spring onions, and sauté until softened.
Add the spinach gradually, letting each handful wilt before adding more.
Sauté until the spinach softens and its liquid evaporates. Transfer to a colander and let it drain completely.
In a large bowl, combine the drained spinach, chopped mint, chopped dill, crumbled feta, beaten eggs, lemon zest, and 1/3 cup olive oil. Season with sea salt and freshly ground pepper. Mix gently.
Preheat the oven to 200°C / 400°F.
Generously brush the baking pan with olive oil. Lay in a phyllo sheet, letting it hang over the edges, and brush with olive oil. Repeat with three more sheets — four in all.
Spread one-third of the filling over the fourth sheet. Place a phyllo sheet on top and gently wrinkle it so it sits inside the pan without hanging over. Brush with olive oil.
Spread another third of the filling. Repeat with one more wrinkled sheet, brushed with oil, and the last third of the filling.
Fold the overhanging phyllo inward over the filling. Top with four more phyllo sheets, brushing each with olive oil. Trim the excess with scissors, leaving about a 5 cm / 2-inch border, and roll it inward to create a frame.
Score the pie lightly into portions without cutting through to the bottom. Bake for about 40 minutes, until golden and crisp. Let stand for 15 minutes before serving.