Prepare the Vegetables: Start by cleaning the celery stalks thoroughly. Remove any tough strings by snapping the stalks and peeling off the fibrous ribs with a vegetable peeler or by hand. Chop the celery and onion into uniform, bite-sized pieces to ensure even cooking. Peel and quarter the potatoes to similar-sized chunks.
Sauté the Aromatics: Heat olive oil in a large soup pot over medium heat. Add the diced onions and cook gently, stirring occasionally, until they turn soft and translucent—about 5 minutes. Stir in the crushed garlic and cook for an additional minute until fragrant, being careful not to burn the garlic.
Combine Vegetables and Broth: Add the chopped celery, potatoes, and parsley to the pot. Pour in the broth and stir to combine all ingredients evenly. Increase the heat and bring the mixture to a gentle boil.
Simmer to Tenderness: Once boiling, reduce the heat to low and cover the pot. Let the soup simmer for around 30 minutes, or until the celery and potatoes are tender enough to mash easily with a fork but not falling apart.
Reserve Celery for Texture: Using a slotted spoon, scoop out a few spoonfuls of the chopped celery and set aside. This will be added back later to provide pleasant texture in the final soup.
Puree the Soup: Carefully blend the soup directly in the pot using an immersion blender until smooth and creamy. If the consistency is too thick, gradually add reserved broth until the desired texture is reached.
Reintroduce Celery Chunks and Season: Stir the reserved celery pieces back into the puréed soup for a touch of crunch. Taste and season with salt and pepper as needed. Serve hot, garnished with extra parsley if desired.