Preheat oven to 425 degrees. Line a large rimmed baking sheet with unbleached parchment paper.
In a large bowl, mix yogurt, oil, spices, garlic, salt, and black pepper.
Bring a large pot of water and a handful of kosher salt to a boil. Add the broccoli to the boiling water for 30 seconds and drain well.
Add broccoli to the yogurt mixture and toss to coat. Arrange in one layer on the prepared baking sheet and roast until browned and the stalks are tender and the yogurt has dried, 20-30 minutes.