Place a rack in top third of oven; preheat to 425°. Bring a small pot of salted water to a boil over high heat. Cut broccoli in half lengthwise, then cut on a diagonal into 2-3 pieces, leaving tips of florets intact. Working in batches, cook broccoli just until bright green, about 30 seconds. Drain very well. (Alternatively, you can skip the blanching process-the broccoli may be a bit tougher in the end but will still be super delicious.)

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).