Preheat oven to 450°F (230°C). Heat the peanut oil in a large, oven-proof sauté pan on medium-high heat. Add the garlic cloves. Add carrots and shiitake mushrooms. Squeeze lime over the contents of the pan. Toss the pan to coat the carrots and mushrooms.
Place the pan in the oven until the carrots and mushrooms are roasted. Your timing will vary based on the thickness of your carrots, which could take anywhere from 15–25 minutes.
Transfer carrots and mushrooms to a plate and let cool. When cool, cut the carrots and slice the shiitake mushrooms. NOTE: You do NOT want to burn your hand on the handle of your sauté pan when you pull it from the oven. Use an oven mitt!
If using the optional sesame soy sauce, whisk together all ingredients for the sauce in a small bowl.
Toss your carrots and shiitake mushrooms with mandarin orange slices and a drizzle of toasted sesame sauce. Garnish your with toasted sesame seeds and season with salt & pepper to taste. Serve over steamed rice as a main or on its own as a naturally vegan side dish. Enjoy!