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Cut zucchini into thin rounds with slicer. Fit slicer with julienne attachment and cut potatoes into ¼-inch-thick matchsticks.
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Start cooking rotini in a pasta pot of boiling salted water (3 Tbsp salt for 6 qt water) according to package instructions. Six minutes before pasta is done, stir in potatoes and green beans. Two minutes before pasta is done, stir in corn and zucchini.
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Meanwhile, heat oil in a 12-inch heavy skillet over high heat until it shimmers. Add tomatoes and cook, covered, shaking skillet once or twice, until tomatoes wilt, split, and release some juices, 3 to 5 minutes. Season with salt and scoop into a small bowl.
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Reserve 1 cup pasta-cooking water, then drain pasta with vegetables.
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Put pesto in a large bowl and whisk in enough reserved cooking water to thin to a sauce, 1/3 to 1/2 cup. Add pasta mixture and toss to coat. Thin with more cooking water and season with salt if necessary. Serve immediately, with tomatoes and bread crumbs on the side.