Bring water to a boil in a large stockpot or Dutch oven. Add squash, cauliflower, carrot, and onions, and cook 2 minutes. Remove vegetables with a slotted spoon; drain well.
Return water to a boil. Add pasta; cook 10 minutes or until done. Drain in a colander over a bowl, reserving 1/2 cup cooking liquid.
Return vegetables to pan; add tomatoes and next 6 ingredients (tomatoes through chickpeas). Cook 2 minutes over medium-high heat, stirring occasionally. Add reserved cooking liquid and wine; cook 15 minutes or until squash is tender, stirring occasionally. Discard thyme sprigs.
Add pasta, salt, and pepper to pan, stirring to combine; sprinkle with parsley.