Heat the oil in a saucepan over low heat. Add the carrot, celery, onion and thyme, season lightly with pepper and cook for 10 minutes. Add the stock and split peas, and bring to a boil quickly over high heat. Reduce heat and simmer until the peas are tender, about 1 hour. Puree 2/3 of the soup in a blender and stir it into the remaining 1/3. If the soup is too thick, thin it by adding a little more stock. Raise the heat and bring the soup to a boil for 15 seconds. Add salt and additional pepper to taste. NOTE: Do not add salt until the peas are fully cooked, because salt will prevent the peas from becoming tender