Heat olive oil in a large stock pot or Dutch oven over medium high heat. Add the onion and a large pinch of salt cook, stirring occasionally, until soft, about 5 minutes. Add the potatoes and vegetable broth, bring to a boil, cover, reduce heat and simmer until the potatoes are tender, about 20 minutes.
Add the oat milk and queso and simmer for about 5 minutes. Blend the soup and taste. Add salt and pepper if needed.