Scrub the burdock roots under cold running water to remove dirt and debris. Leave the skin on since a lot of the nutrients are there.
Cut burdock root and carrot into matchstick sizes.
Transfer burdock and carrot matchsticks into a bowl of cold water and set aside.
Heat oil in a large skillet over medium-high heat.
Add gobo and carrots and cook, stirring for about 2 minutes.
Add coconut sugar, lime juice, and Bragg's Liquid Aminos, and continue to cook, stirring.
Check Gobo to see if it is tender; if not, add vegetable broth starting with 1/4 cup and cover the skillet to cook until Gobo is tender.
Sprinkle with sesame seeds and serve.
Store leftovers in the refrigerator for 2-3 days.