Make the cheese sauce first, or make it ahead of time. This recipe makes about 4 cups of cheese sauce, and you only need 2 cups for this recipe.
Wash and cut carrots and potatoes into quarters (leave the skins on)
Put into a pot and bring water to a boil; reduce heat to medium and boil for 30 minutes
Drain potatoes and carrots
Add all other cheese ingredients to a high-speed blender
Add potatoes and carrots to the blender, and blender until smooth
You may need to add more veggie broth if too thick (this will depend on the size of the carrots/potatoes you used)
While the 'cheese' sauce is blending, sauté the shallot, garlic, and onion until translucent
Put Frozen Hash Browns in a large bowl
Add onion/shallot/garlic/pepper mixture
Add 2 cups of cheese sauce
Mix with a spoon so all the potatoes are coated with 'cheese' sauce
Transfer vegan hash brown mixture to a 9 X 13-inch pyrex pan or casserole dish