Heat the oil in a large pot over medium-high heat. Add the poblanos, onion, garlic, and ½ teaspoon each salt and black pepper. Cook, stirring, until softened, 10 to 12 minutes. Add the zucchini and tomatoes (and their juices). Cook, stirring, until the zucchini is crisp-tender, 12 to 15 minutes.
Add the shrimp, corn, and 3 cups water. Bring to a simmer. Cook, stirring occasionally, until the shrimp are white throughout and the corn is tender, 5 to 6 minutes. Sprinkle with black pepper and serve.
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