1. Heat oven to 400 degrees. Line a large baking sheet with a clean dishtowel or several layers of paper towels and spread drained chickpeas evenly on top. Pat dry with another dishtowel or paper towels.
2. Toss sweet potato and carrots with 2 tablespoons oil and season with 3/4 teaspoon salt and 1/4 teaspoon pepper. Spread on a large rimmed baking sheet and top with thyme sprigs. Roast, tossing occasionally, until golden-brown and very tender, 40 to 50 minutes.
3. While vegetables are roasting, toss chickpeas with 2 tablespoons oil, chili powder, cumin and a large pinch of salt. Spread on another rimmed baking sheet. Transfer to the oven 10 minutes after you’ve put in the potatoes and carrots; roast until crisp and golden brown, 30 to 40 minutes.
4. Using the flat side of a knife or a mortar and pestle, mash the garlic with a large pinch of salt until it forms a paste. Add it to a small bowl and whisk in yogurt and lemon juice. Slowly whisk in remaining 4 tablespoons (1/4 cup) oil. Season with salt and pepper.
5. In a large bowl, combine spinach, roasted vegetables, chickpeas and shallot. Toss with enough dressing to lightly coat vegetables and greens and serve at once.
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