Heat the oil in a medium-sized pot. Add the celery, onion and leek. Cook over medium-low heat, stirring occasionally, until soft but not browned, about 6-7 minutes. Add the stock, salt and pepper to taste and simmer until the vegetables are very tender, about 15 minutes. With a slotted spoon, transfer the vegetables to a blender (reserving the stock).
In the meantime, bring a medium saucepan of salted water to a boil. Add the sugar snap peas and cook for 3 minutes. Add the baby peas and parsley and cook for another minute. Drain.
Add the cooked peas and parsley to the blender with the other vegetables. Process until very smooth.
Blend in stock, little by little, until desired consistency is reached. Taste soup and season with salt as needed.
Chill in the refrigerator.
Ladle the chilled soup into individual bowls and top with desired garnishes.