Heat the olive oil and butter in a large Dutch oven over medium-low heat. Add the onions and celery and cook for 5-6 minutes, stirring often, until tender. Do not let the onions brown.
Add the potatoes, chicken broth, sea salt, and white pepper to taste. Simmer over medium-low heat for 30 minutes.
Once the potatoes are tender, mash them slightly with a potato masher, leaving most of them in chunks. Reduce the heat to low, then stir in the half and half, cheese, and sugar to the soup.
Stir until the cheese has completely melted and dissolved into the soup. Taste and re-season with salt and white pepper, if needed.
Simmer for 10-15 minutes–don't let the soup boil, or it will curdle.
Serve topped with chives, bacon, and more cheddar cheese. Serve immediately and enjoy.