Cook bacon until crisp in 3-quart saucepan, remove and drain well on paper towels. Discard bacon grease and wipe pan thoroughly.
Meanwhile, prepare vegetables. Add olive oil to saucepan and add onion, carrot and celery as they are cut up. Saute until onion is soft but not brown, about 3-4 minutes.
Stir in chicken broth, potatoes and cayenne pepper; bring to a boil, reduce heat and simmer, until potatoes are tender, about 10-15 minutes.
Stir in cheddar cheese, heating just until melted - do not boil. Chop bacon and add to soup. Season with salt as necessary.