Preheat the oven to 425°F (220°C). Line an extra-large (15 by21-inch/38 by 53 cm) baking sheet with parchment paper.
Chop the zucchini, onion, and bell peppers into 1⁄2-inch (1 cm) pieces and slice the carrots crosswise into 1⁄4-inch-thick (5 mm)coins (it’s important to cut the vegetables to the specified sizes so they cook within the appropriate time frame), adding them to the prepared baking sheet as you go. You should have 2 cups zucchini, 1 1⁄2 cups onion, 3 cups bell peppers, and 1 1⁄4 cups carrots. Put the garlic cloves on a square of aluminum foil, drizzle with 1 teaspoon of the oil, and fold the foil to completely enclose the garlic.
Toss the veggies with 2 tablespoons of the oil until thoroughly coated. Sprinkle with the salt and pepper. Place the foil packet with the garlic on the baking sheet.
Roast the veggies and garlic uncovered, for 40 to 45 minutes, until the veggies are lightly charred (this adds mega flavor!)and fork-tender. You can remove the garlic a bit earlier to avoid burning it, if necessary. After cooking, carefully unwrap the garlic and discard the foil.
Meanwhile, bring a large pot of water to a boil. When the veggies have about 10 minutes left in the oven, add the pasta to the boiling water and cook until al dente according to the package directions. Drain the pasta and return it to the pot.
In a high-speed blender, add the fire-roasted tomatoes with their juices, the roasted veggies and garlic, and the remaining1 tablespoon oil. Blend on medium speed until smooth. (Depending on the size of your blender, you may have to do this in a couple of batches.) The sauce will be luxuriously thick.
Add your desired amount of sauce to the pot with the drained pasta and stir to combine. Depending on how much pasta you prepared, you may have sauce left over, so be sure to see the storage information. Stir in the vinegar to taste (start with 1⁄4 teaspoon and add more little by little from there) and season with additional salt and pepper, if needed. Stir in the basil (if using—if you have a picky eater who might spot that speck of green and gasp, you can sprinkle it over individual plates instead). Cover and simmer over medium heat for about 5 minutes to allow the flavors to develop even more. Serve and enjoy!