Preheat oven to 425°. Mix vadouvan, half of garlic, 1/4 cup yogurt, and 3 tablespoons oil in a large bowl until smooth; season with salt and pepper. Add carrots and toss to coat. Roast on a rimmed baking sheet in a single layer, turning occasionally, until tender and lightly charred in spots, 25-30 minutes.
Meanwhile, heat turmeric and remaining 2 tablespoons oil in a small skillet over medium-low, swirling skillet, until fragrant, about 2 minutes. Remove from heat.
Whisk lemon juice, remaining garlic, and remaining yogurt in a small bowl; season with salt and pepper.
Place carrots (along with crunchy bits on baking sheet) on a platter. Drizzle with yogurt mixture and turmeric oil and top with cilantro. Serve with lemon wedges.