Pre-heat oven to 425 degrees and line a baking dish with foil.
Place carrots in a large resealable plastic bag and drizzle with olive oil.
In a medium bowl, mix together all of the spices: cinnamon through allspice. Place half of the spice mixture in the bag with the carrots and shake until evenly coated. Spread the carrots evenly on prepared baking sheet and roast until tender and caramelized, 20-25 minutes.
While the carrots are roasting, prepare the yogurt dressing by adding the yogurt, lemon juice and garlic into the bowl with the remaining spices. Whisk until smooth and creamy; set aside.
Serve the carrots on a platter and drizzle with yogurt dressing to serve. Can be served warm, room temperature or chilled.