Cook the pasta according to package directions in salted water, to al dente, then drain.
Meanwhile, add broccoli and peas to a large pan with vegetable broth. Cover and bring to a simmer, cook for 3 to 4 min then remove lid and cook another couple minutes to allow liquid to evaporate. The broccoli should be crisp-tender, so drain away any liquid that remains.
While those are cooking, chop the tomatoes, peppers and olives. Add these to the broccoli and peas once those are done. Whisk together the dressing, and add it to the pan along with the cooked pasta and parmesan. Stir well, taste for seasoning.
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