Roast the carrots: Preheat oven to 400 degrees F and line a large baking sheet with parchment paper. Set aside. Depending on the type of carrots you are using, peel and cut each carrot down the middle lengthwise if necessary. Spread the carrots in an even layer over the prepared baking sheet. Drizzle with olive oil and sprinkle with salt and pepper. Carefully mix carrots in the olive oil so that they are evenly coated. Roast carrots in the middle rack for 25-30 minutes, or until fully cooked and starting to brown on the tops and edges.
Make the Sauce: Meanwhile, prepare the sauce by mixing together the yogurt, tahini, lemon juice, salt and pepper and garlic. Add a couple tablespoons of water, if needed, to reach desired consistency.
Remove carrots from the oven and drizzle with your prepared lemon tahini sauce. Sprinkle with parsley and serve immediately.