Heat the oven to 425°. Warm a large nonstick skillet over medium heat. Add 2 teaspoons of the oil, swirling it to coat the pan. Add the spinach (in batches, if necessary) and sauté it until it is just wilted, about 2 minutes. Transfer the spinach to a plate to cool, about 10 minutes.
Meanwhile, add another 2 teaspoons of oil to the skillet, then add the onion, scallions, and garlic. Sauté them until they have softened, about 2 to 3 minutes. Let them cool in the pan for about 10 minutes.
Lightly beat the egg in a medium bowl, then whisk in the salt, pepper, nutmeg, dill, and parsley. Stir in the cooled onion mixture. Gently squeeze handfuls of the spinach over the sink to remove the excess moisture. Add the spinach to the bowl, then crumble in the feta, stirring gently to combine the ingredients.
Brush a large, heavy baking sheet with 1 teaspoon of the remaining oil. Arrange the tortillas on a work surface. Sprinkle a generous tablespoon of the mozzarella over half of each tortilla. Top the mozzarella with a quarter of the spinach mixture, distributing it evenly and leaving a thin border at the edge. Sprinkle another tablespoon of the mozzarella over the spinach, then fold each tortilla in half. Set them on the baking sheet and brush the tops and edges with the remaining teaspoon of oil.
Bake the spanakopadillas on the top rack for 10 minutes. Remove them from the oven, flip them over, and let them rest bottom side up on a cutting board for 5 minutes. Cut each tortilla into thirds.