In a dutch oven, heat avocado oil. Add in onion and saute until softened.
Add in garlic and let cook 2 minutes.
Using a whisk, add in the flour, then the chicken stock until well combined and no clumps.
Bring to a boil, then add the broccoli, carrots, salt, pepper, and nutmeg and cook for 10 minutes.
After 10 minutes, add the milk and the cheese. Lower heat to medium and stir.
In a small dish, whisk together the arrowroot and milk to create a slurry, then pour it into the soup. This will help thicken your soup greatly. Let soup cook for 10 minutes over medium-low heat.
Turn off heat and serve!