To prepare sauce, in large non-stick saucepan, heat oil and butter over medium-high heat 30 seconds. Add broccoli, onions, and carrot and sauté until carrot is tender, 5 minutes. Add mushrooms, squash, and garlic; sauté 2 minutes longer.
Add 1 1/2 cups water and the next 7 ingredients; cook, stirring until just below boiling. Lower heat, cover and simmer until vegetables are tender, 8-10 min.
Meanwhile, cook pasta in large pot of boiling water until tender, 6-8 minutes. Drain and place in serving bowl. Toss with sauce and sprinkle with cheese.