Heat the sunflower oil in a large pan and gently fry the onion with a larger pinch of salt for about 10 minutes. Add garlic, black pepper and thyme and cook for a few minutes. Add carrots and parsnips and then pour the broth, bring to a boil and cook for 20 minutes until the vegetables are soft.
Pour the cream and mix the soup with a hand mixer until completely smooth. Taste and divide between the four bowls, and if you want to garnish with cream.