First, prepare the filling. In a medium pot over medium-high heat, warm up the garlic and olive oil until it starts to sizzle slightly.
Tear the spinach leaves and baby kale leaves roughly with your hands, and throw them into the pot, a bit at a time, until they are all reduced and wilted down.
Add in the seasonings, mix well, then remove from heat. Let the vegetables cool down slightly, then pour them in a colander or sieve and press out as much of the watery liquid as possible.
In a large bowl, whisk together the ricotta, mozzarella, Parmesan, and a bit more salt and pepper. Beat 5 of the eggs in a small bowl, set 1-2 tablespoon aside for the egg wash later, then add the rest into the cheese mixture. Stir in the strained spinach and kale.
Now, preheat the oven to 340F and prepare the crust. In a 9-inch deep dish pie pan, layer 10 of the phyllo sheets, spraying every other one with olive oil.
Pour the spinach filling into the crust, and using a spoon, make 5 deep indentation evenly around the pie. Crack an egg into each indentation and sprinkle lightly with salt.
Top the pie with the remaining 10 sheets of phyllo, again spraying every other one with the oil.
Go around the edges and lightly crimp the layer of phyllo closed, then brush with the egg wash you saved from earlier. Using a sharp knife, make 8 small cuts in the center to let the steam out.
Place in the center rack of the preheated oven, and bake for 70-80 minutes, until pie is golden brown and there is no jiggle in the center.
Let cool slightly, then slice and enjoy!