Preheat the oven to 375F. In a large nonstick pan, heat 2 tablespoons of olive oil over medium high heat. Add in the onion, garlic, and carrot and cook until tender, about 5 minutes. Next, add in the crushed tomatoes and seasonings and simmer for 15 minutes. Taste and adjust the seasoning with salt and pepper. Once the sauce has thickened, pour into a 2 quart baking dish. Arrange the sliced vegetables in a circular pattern standing upright in the dish over the sauce. Brush with the remaining olive oil. Cover and bake for 30 minutes, then uncover and bake until vegetables are tender. Serve immediately.