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Preheat oven to 400°F.
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Slice zucchini, yellow crookneck, and pattypan. Chop basil, about 4 tablespoons. Chop shallots. Cut cherry tomatoes in half.
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Place four 14x12" sheets of parchment paper, or heavy-duty foil, on a work surface. Divide squash among parchment sheets, arranging on one side of sheet in thin layers.
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Sprinkle shallots and sliced basil over. Scatter tomato halves around squash. Drizzle each packet with 1 tablespoons wine and 1/2 tablespoon oil. Season with salt and pepper.
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Place a fish fillet atop each portion. Season with salt and pepper; drizzle 1/2 tablespoon oil over each.
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Fold parchment over mixture and crimp edges tightly to form a sealed packet. Place packets in a single layer on a large rimmed baking sheet.
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Bake or grill fish until just cooked through, about 10 minutes. Carefully cut open packets (steam will escape). Garnish with basil leaves.