1. Peel the garlic cloves, halve them and remove any green shoots; put them in a small saucepan, cover with the milk and simmer over low heat for 20-25 minutes until completely soft (this mellows their flavour).
2. Finely chop the anchovy fillets (if salted, rinse them and remove the bones).
3. Drain the garlic (discard the milk), put it in a heavy-based pan - ideally earthenware - with the olive oil and mash it to a paste with a fork.
4. Add the anchovies and warm over the lowest heat, stirring constantly, for 10-15 minutes until they have completely melted - make sure it doesn't fry, only melts slowly; finally stir in the butter.
5. Meanwhile prepare the vegetables: boil the potatoes in their skins and cut into wedges, and cut the pepper, carrots, celery and fennel raw into sticks.
6. Serve the dip warm, kept over a small tea light, for everyone to share, and dip the vegetables into it.
Tip: In Piedmont it's eaten in autumn at harvest festivals, from a shared earthenware pot; at the end you can scramble an egg in the leftover sauce, and fresh bread is a must alongside.
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