Add oil to a large pot set over medium-high heat. Add onion and celery and saute for 2 to 3 minutes, or until they start to soften. Add stock and mashed potatoes and bring to a simmer.
Using a hand blender or regular blender, puree soup until smooth (when using a regular blender, work in batches to prevent messy cleanups!). Add Cheddar, salt, white pepper, dry mustard and hot sauce. Stir to combine and allow the cheese to melt.
Recipe courtesy of Bobby Flay