Heat olive oil in a large pot over medium heat. Sauté onion, green onions, and celery for 5 minutes. Add garlic and diced potatoes to the pot.
Pour in the vegetable broth and add the green beans. Bring the mixture to a boil, then reduce the heat, season, and let it simmer for 30-40 minutes.
Use an immersion blender to blend the soup until it’s completely smooth or has some chunks left, as desired.