Add spinach, salt, black pepper, and nutmeg to a 12-inch sauté pan over medium heat. Cover and cook until spinach has wilted, about 3 to 5 minutes. Allow the spinach to cool slightly.
Once cooled, squeeze the spinach in a fine mesh strainer or clean tea towel to remove excess moisture.
Chop the spinach finely.
To assemble quesadillas, distribute half of the mozzarella cheese over one half of each tortilla.
Top with spinach, then sprinkle with crushed red pepper flakes and oregano.
Add feta cheese, remaining mozzarella, and a sprinkle of garlic powder. Fold tortillas to form half-moons.
Heat olive oil in a large non-stick frying pan over medium-low heat. Cook quesadillas in batches, about 3-4 minutes per side, until golden brown and cheese is melted.
Serve hot, cut into halves, optionally with Greek yogurt.
