Place a large soup pot on the stove over medium high heat. Add in olive oil and onion and saute until tender, about 7 minutes. Add in garlic and ginger and saute 1 minute more.
Add in sweet potatoes and season with salt and pepper. Pour in vegetable broth and bring to a boil over high heat. Once boiling, reduce the heat to medium and simmer until sweet potatoes are tender, about 10-15 minutes.
Transfer the soup mixture to a blender and blend in batches until smooth, or use an immersion blender.
Return to a pot over low heat and add in the cheddar cheese. Stir until melted. Taste and add more salt if desired. Serve topped with green onions or chives.