Preheat the oven to 350 F. Grease a 3-quart baking dish or 9-by-13-by-2-inch baking pan.
Heat 2 tablespoons of vegetable oil in a large skillet over medium heat. Add half of the onions and cook for 2 minutes. Add the garlic, zucchini, and mushrooms, along with another tablespoon of oil and continue to cook for 3 minutes.
To the skillet add the chicken, rice, stock, thyme, rosemary, and Parmesan cheese. Add kosher salt and pepper to taste. Turn the mixture into the prepared baking dish.
Heat the remaining 1 tablespoon of oil in the skillet and add the remaining onions. Cook the onions for 3 minutes. Add the tomatoes and chili powder and season to taste with salt and pepper. Spoon the tomato mixture over the chicken and rice mixture.