Preheat oven to 180°C (356°F). Toss zucchini cubes with olive oil, salt, and pepper. Roast until tender. Heat olive oil in a large skillet over medium-high heat. Add leeks, white onion, and green bell pepper.
Sauté until softened. Add roasted zucchini, diced tomatoes, hearts of palm puree, turkey, hearts of palm spaghetti, oregano, basil, thyme, chili pepper, salt, and pepper to the skillet.
Stir to combine. Transfer the mixture to a baking dish. Sprinkle with Parmesan cheese. Bake at 180°C (356°F) for 10 minutes, or until cheese is golden brown.