Combine the chicken broth, coconut milk, vinegar, arrowroot, and nutritional yeast in a bowl and set aside.
Using a large pot, heat the avocado oil over medium heat. Add the garlic, onion, carrot, and sweet potato and saute for 7-8 minutes or until lightly tender.
Pour the liquid over the vegetables and stir to combine. Bring to a boil and reduce to a simmer for 20-25 minutes or until the vegetables are soft.
Allow to cool slightly before blending in a blender or with an immersion blender. See notes for adjusting taste or thickeness.
Serve warm over vegetables, or as you would a cheese sauce.