Thaw phyllo dough following package directions.
Preheat oven to 400 degrees.
Peel and seed winter squash. Cut into 1-inch pieces.
Place on a parchment lined baking sheet and bake in oven for about 30 minutes, or until squash is tender. Remove from oven and cool. Reduce oven temperature to 375 degrees.
In a large bowl, mash cooked squash. Add parsley, mint, and Feta. Stir to combine.
Wash and chop the white and light green parts of the leek. Peel and mince the garlic.
Heat a little olive oil (about 2 teaspoons) in a small frying pan. Add the chopped leek and garlic. Cook until just tender, about 5 minutes. Remove from heat. Add to the squash mixture.
Grease an 8-inch cake pan. Layer 7 sheets of phyllo dough, brushing each with olive oil, and overlapping each sheet until the entire cake pan is covered.
Stir a beaten egg into the squash mixture. Spread mixture over the phyllo in the pan.
Cover with 5 sheets of phyllo dough, once again brushing each sheet with olive oil. Tuck the edges into the side of the pan. Make a few cuts in the top with a knife.
Bake for 45 minutes, or until the pie is golden brown. Remove from oven and serve warm or at room temperature.
Note: This recipe will use less than one package of commercial phyllo dough. Save the remainder for another pie or refreeze for future use.