Preheat the oven to 350 degrees F.
Heat the extra-virgin olive oil in large pot over medium heat. Saute the garlic, leeks and shallots until soft, about 5 minutes. Add the spinach and scallions and cover the pot for a few minutes until spinach has wilted significantly. Uncover and simmer on medium-low heat to allow the liquids to evaporate (be sure not to let spinach mixture to burn). When the majority of the liquids have evaporated, transfer to a large bowl. Mix the feta, ricotta, kefalotiri, dill, mint, pepper, nutmeg and eggs in a large bowl. Gently fold the cheese mixture into the cooled spinach mixture.
Brush a 15-by-10-inch rectangular pan with olive oil. Gently place one sheet of number-10 phyllo in the bottom of the pan and brush with olive oil, making sure to coat well. Repeat this step eight times. This creates a nice strong base for serving.
Pour in the spinach filling. Use the entire box of number-7 phyllo on top of the spinach, making sure to coat each layer of dough very well with olive oil. Also make sure to tuck in edges of the phyllo around the pan to make it look pretty. Score the pie in appropriate portion sizes. Brush the top with the beaten eggs; this gives it the beautiful golden brown color that is achieved after approximately 1 hour of baking.
Cover the phyllo dough as you are working with a slightly moist kitchen towel to keep it from drying out. Be sure to work quickly.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.