Preheat the oven to 350°F. Spray an 8x8-inch casserole dish with nonstick cooking spray.
Cook the pasta in a pot of salted water according to the package directions for al dente consistency. Drain and set aside.
Heat a large skillet over medium-high heat and add the olive oil. When the oil is hot, add the onion. Cook for 3 minutes, stirring frequently, until softened. Add the garlic and cook for an additional 30 seconds.
Add the spinach leaves and cook for 2 minutes, until wilted. Remove from heat and stir in the sliced zucchini.
Stir in the balsamic vinegar, basil, oregano, sugar, salt, and black pepper.
Add the feta cheese and 1/2 cup mozzarella cheese; stir gently to combine. Stir in the cooked pasta.
Adjust seasoning to taste then transfer to the prepared baking dish. Sprinkle with the remaining 1/2 cup mozzarella cheese.
Bake for 20 minutes, until the cheese is melted. Sprinkle with parsley and serve.