Heat oil in a large saucepan or medium pot over medium high heat. Add onion and garlic, and saute until soft (few minutes).
Add potato and broth, and bring to a boil. Cover, reduce heat to low and simmer for 20 minutes.
Remove 2 cups of mixture with a slotted spoon and set aside. Pour the rest in a blender and blend until smooth.
Return everything to saucepan. Add vegan cheese, non-dairy milk, and parsley. Cook until cheese is melted. Serve.

2 teaspoon olive oil
2 teaspoon minced fresh garlic
2 cup diced onion
3 pound potatoes, peeled and cubed
6 cup vegetable broth
2 cup vegan cheddar cheese
1 cup non-dairy milk (soymilk)
1/2 cup fresh parsley, chopped
salt, to taste