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Preheat oven to 400 degrees. On a rimmed baking sheet, toss together bread, 1 tablespoon oil, and Parmesan. Season with salt and pepper. Bake until golden and toasted, 8 to 10 minutes.
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Meanwhile, in a large pot of boiling salted water, cook pasta 2 minutes less than package instructions; add broccoli and cook 2 minutes. Reserve 1/2 cup pasta water, then drain.
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Add remaining 3 tablespoons oil and garlic to pot and cook until garlic is fragrant and lightly golden, 1 to 2 minutes. Add pasta mixture; toss to combine, adding enough pasta water to create a light sauce that coats pasta. To serve, sprinkle with croutons, lemon zest, and additional Parmesan if desired.