Heat the butter in a pan and gently fry the shallot until softened but not coloured. Add the new potatoes and fennel and sauté for 2-3 minutes. Add the stock and bring to the boil. Reduce the heat and simmer for 8-10 minutes, or until the vegetables are tender.
Preheat the oven to 180°C. Put the carrots, fennel and onion in a roasting dish and toss with 2 tablespoons of olive oil. Roast for 20 minutes, then add the garlic cloves. Stir everything thoroughly and return to the oven for 20 minutes more, until the vegetables are soft and browned.
Slice each part across quite thinly (into approx. 5mm strips). In a large pot heat up the oil, butter and fennel seeds and cook gently until the butter has melted. Add the onion, garlic, celery and fennel, season lightly, stir and cook over a medium heat for about 5 minutes stirring often.
Mild onion and anise flavored - it's awesome! Melt the butter in a large skillet over medium heat. Add the quartered fennel bulbs; cook and stir until golden brown, about 10 minutes. Pour in the broth, and simmer until fennel is tender, about 15 more minutes. Ladle into soup bowls, and season with salt and pepper.