Preheat the oven to 375°. In a bowl, toss the kale with all but 1 tablespoon of the olive oil and half of the garlic. Spread the kale on 2 baking sheets and roast in the upper and lower thirds of the oven for about 15 minutes, until crisp; shift the pans from top to bottom halfway through. Season the kale with salt and pepper and transfer to a large platter.
In a small bowl, whisk the yogurt with the lemon zest and juice and the remaining garlic and 1 tablespoon of oil. Season with salt and pepper. Serve with the roasted kale.