Place the chopped leeks and white part of the green onions in a colander. Wash thoroughly, then season with salt, pepper, sugar, and nutmeg. Let them sit to release their natural liquids.
In a small pan, heat a little olive oil. Cook the chicken pieces with salt and pepper until they start to get color. Turn off the heat, add the green part of the green onions, and let cool.
Drain the leeks and onions well. Combine with the cooked chicken, crumbled feta, parsley, and dill. Set aside.
Preheat the oven to 200°C (392°F). Brush a baking tray with olive oil and place a sheet of parchment paper on it.
Lay out 5 phyllo sheets, brushing each generously with olive oil. Spread the filling evenly over the phyllo.
Cover with the remaining 5 phyllo sheets, brushing each layer with olive oil. Fold and seal the edges neatly.
Using a sharp knife, score the top into portions. Cover with aluminum foil and bake for 40 minutes.
Remove the foil and bake for another 20 minutes until the top is golden and crisp.
Allow to cool slightly before serving.