Preheat the oven to 350 degrees F. Lightly coat a 8- by 12-inch or 2 quart baking dish with cooking spray.
Heat the olive oil in a large nonstick skillet set over medium-high heat. Add the ground turkey, onions, ½ teaspoon salt and ¼ teaspoon ground pepper. Cook, breaking up the turkey with a wooden spoon, until the turkey is browned.
Stir in the mushrooms, zucchini, garlic, oregano and red pepper flakes, and cook until the vegetables are starting to soften, 3 to 4 minutes.
Stir in the crushed tomatoes and the remaining ¼ teaspoon salt and ¼ teaspoon ground pepper. Bring the mixture to a boil, then reduce heat and simmer for 10 minutes, stirring occasionally.
Stir in the rice, ¼ cup Parmesan cheese and 3 tablespoons parsley.
Transfer the mixture to the prepared baking dish. Sprinkle the remaining ¼ cup Parmesan cheese on top and bake until the casserole is bubbling and the cheese is melted and starting to brown, about 20 minutes.