Meanwhile, whisk yogurt, oil, paprika, coriander, turmeric, garlic, and cayenne in a medium bowl. Season with salt. Add broccoli and toss to coat. Transfer broccoli mixture to a foil-lined rimmed baking sheet and arrange in a single layer. Roast broccoli until browned and stalks are tender, 15–20 minutes (unblanched broccoli may take as long as 25 minutes).
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