For the creamy fennel soup, cut off the heads from the fennel bulbs and keep them. Cut out the stalk from the fennel bulbs and cut the rest into equal-sized pieces.
Peel and chop the garlic cloves and shallots. Heat olive oil in a pot, add shallots and garlic and sauté. Then add the fennel and sauté.
Then fill up with vegetable soup and add the Pernod. Cover and simmer for about 20 minutes. Then puree with a hand blender and add whipped cream.
Season to taste with salt and pepper. Divide the creamy fennel soup among four pre-warmed bowls and garnish with the fennel greens.