Preheat the oven: Set your oven to 450°F. On one or two large baking sheets, toss the zucchini slices with 3 tablespoons of olive oil and a pinch of salt. Spread them out evenly, then roast for approximately 40 minutes, stirring halfway through, until the zucchini is deeply browned.
Cook the onions: Heat 1 tablespoon of olive oil in a 10-inch ovenproof skillet over medium heat. Add the sliced onions along with a pinch of salt and pepper. Sauté until the onions become soft and golden, about 10 minutes.
Add anchovies and spices: Stir the chopped anchovies, minced garlic, oregano, and red chili flakes into the skillet with the onions. Cook for 2–3 minutes, or until the anchovies have dissolved into the mixture. Once done, combine this mixture with the roasted zucchini in a large bowl. Reduce the oven temperature to 400°F and let the zucchini mixture cool slightly.
Prepare the filling: In a separate bowl, whisk the eggs together. Stir in the chopped fresh herbs (mint, parsley, or dill) and chives. Pour this egg and herb mixture into the cooled zucchini mixture, and add the lemon juice, adjusting the flavor with more juice if needed.
Assemble the pie: Clean the skillet and brush it generously with olive oil. Place two sheets of phyllo dough into the skillet, arranging them so the edges hang over the sides. Layer two more sheets perpendicularly, creating a crisscross pattern. Spoon the zucchini mixture into the center of the skillet. Fold the phyllo edges over the filling, lightly crumpling them to create texture. Layer the last two sheets of phyllo on top for a decorative, uneven effect. Brush the phyllo with olive oil, ensuring all layers are well-coated, and sprinkle with a pinch of salt.
Bake the pie: Transfer the skillet to the oven and bake for 35–40 minutes at 400°F, or until the phyllo is crisp and golden brown. Remove from the oven and let the pie cool slightly. Serve warm or at room temperature, garnished with fresh dill or additional herbs.