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.