In a medium bowl, combine the crumbled feta, chopped spinach, halved cherry tomatoes, sliced red onion, parsley, dill, olive oil, dried oregano, and black pepper. Gently mix until everything is evenly coated.

Lay out 4 tortillas on a clean surface. If using, sprinkle about 2 tablespoons of shredded mozzarella evenly over each tortilla. Divide the Mediterranean filling evenly among them, spreading it over one half of each tortilla, leaving a 1-inch border. Fold the empty half over the filling to create a half-moon shape. Press gently.

Heat a large skillet, grill pan, or non-stick pan over medium heat. Lightly brush the outside of one quesadilla with olive oil. Place it oil-side down in the hot pan. Cook for 2-3 minutes until the tortilla is golden brown and crispy. Brush the top side with oil, then carefully flip using a spatula. Cook for another 2-3 minutes until the second side is golden and the cheese is melted. Repeat with remaining quesadillas.

Transfer each cooked quesadilla to a cutting board. Let rest for 1 minute, then slice each into 3 triangles. Stack the triangles on a serving plate. Serve immediately with dollops of Greek yogurt, scattered kalamata olives, a sprinkle of fresh mint, and lemon wedges on the side.