In a large saucepan, cook the celery, carrots, and apple in the oil over medium heat until softened, 7 to 8 minutes. Add the chicken broth and potatoes; cover. Heat to boiling. Reduce heat to low, cover, and cook until the potatoes are tender, about 15 minutes.
Puree the soup in a blender or food processor. Return to saucepan and whisk in the Cheddar and Worcestershire. Season to taste with salt. Serve with croutons or crusty bread.