Separate 3/4 cup of cauliflower florets and place them in a pan of boiling water. Boil for 2 to 3 minutes, then rinse under cold water and set aside for garnish.
Heat oil in a large saucepan over medium heat. Add celery, leek, onion, and garlic; cook and stir until tender, about 5 minutes. Add chicken broth, remaining cauliflower, potato, and sherry. Bring to a boil; simmer over low heat, stirring occasionally, until potatoes and cauliflower are tender. Remove from heat.
Purée cauliflower mixture in batches using a food processor or blender; transfer to a soup pot over medium-low heat. Season with white pepper, black pepper, and salt. Stir in milk and cream, then crumble in Stilton cheese. Heat through, but do not boil.
Ladle into bowls, and garnish with reserved cauliflower pieces and chopped fresh parsley.