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 potato and bring to a boil.
Reduce heat to low and simmer, covered, until the potato is tender, about 15 minutes.
Puree the soup in a blender or food processor. Return to saucepan, whisk in the Cheddar and Worcestershire, and season to taste with salt.
Serve the soup with croutons or bread (if desired).