Preheat your oven to 375°F (190°C) and lightly grease a small individual-sized baking dish.
Heat the olive oil in a skillet over medium heat, then sauté the diced onion and minced garlic until translucent and fragrant.
Add the fresh spinach to the skillet in batches, stirring until completely wilted.
Transfer the spinach mixture to a clean kitchen towel or fine-mesh sieve and squeeze out as much liquid as possible to prevent a soggy crust.
In a mixing bowl, combine the shredded chicken, squeezed spinach mixture, crumbled feta, egg whites, chopped dill, nutmeg, salt, and pepper.
Lay one sheet of phyllo dough into the baking dish, allowing the edges to hang over, and lightly mist with oil; repeat with the second sheet.
Spoon the chicken and spinach filling into the center of the dough and spread it evenly.
Fold the overhanging phyllo edges back over the filling to create a rustic crust.
Bake for 25 to 30 minutes until the phyllo is golden brown and the filling is set.