Heat oil in a (4-quart) pot over medium heat. Add celery, onion, and potato, season with salt. Cook, stirring occasionally, until vegetables begin to soften, about 8 minutes.
Add the mince garlic and fresh rosemary and cook for 30 more seconds.
Pour in the chicken stock, bring to a boil, reduce heat and let simmer until vegetables are tender about 20 minutes.
Add the grated cheese and stir. Use either an immersion blender, food processor or blender to puree until smooth. If using a food processor or blender, you will need to work in batches.
Add salt and pepper to taste. Serve with extra grated cheese for garnish.