In a large non-reactive pot, melt butter and sauté onions and garlic until soft; do not let them brown! Add potatoes and garlic, stir to coat with butter and cook about 4 minutes. Add stock to cover, lower heat, and simmer until potatoes are tender, about 30-40 minutes. Remove from heat and allow it to cool a bit.
Blend smooth with a hand blender, or transfer to a blender and process until smooth. Return it to the pot if you are using a blender. Stir in the cream and cheese. Ladle the soup into bowls and garnish with the reserved cheese.
Recipe by Have You Eaten, SF? at https://haveyoueatensf.com/potato-onion-and-cheddar-soup-a-tale-of-two-soups/