Melt the butter with olive oil in a large soup pot or Dutch oven over medium heat.
Cook and stir the celery, carrots, and garlic until soft, about 8 minutes.
Pour in the chicken stock, beer, Worcestershire sauce, hot pepper sauce, white pepper, mustard powder, onion powder, garlic powder, and cayenne pepper; whisk to combine.
Blend the mixture with a hand blender until smooth. Bring to a boil, reduce heat to low, and simmer 15 minutes.
Stir in the cream of chicken soup and the Cheddar cheese soup; bring soup back to a simmer.
Stir in the processed cheese and allow to melt. When it has melted, slowly mix in the pepperjack and sharp Cheddar cheeses, a little at a time, allowing each addition to melt into the soup before adding the next.
Simmer the soup over low heat until the cheese has completely melted and the flavors have blended, 15 to 20 more minutes.
