In a large skillet or chef pan add oil and heat over medium heat. Add your onion and carrots and cook until the onions are soft. At this point, you can add the garlic and cook for another 1-2 minutes, until fragrant.
Add the broccoli, zucchini and marinara. Simmer for 4-5 minutes, stirring often to ensure the sauce doesn't splatter too much. While this is cooking, take a fork and scoop out the spaghetti squash into a bowl (you should have roughly two cups) and add to the sauce, along with the Parmesan cheese.
Transfer to a casserole dish (a 9x13 would work fine) and bake for 10 minutes. Top with cheese and bake until brown and bubbly.