Place the garlic cloves in a saucepan and cover with 100ml (1/4 cup + 2 tbsp) of the milk. Leave to soak for 1 hour, drain and discard the milk. Place the garlic back in the saucepan with the rest of the milk and 1 tbsp of water. Gently cook, partly covered with a lid, over a low heat for 20 minutes until the garlic is super tender.
Add the chopped anchovies to the pan and cook, stirring until they have broken down. Add the butter and stir until melted. Pour this into a blender along with the drained beans, creme fraiche/cream, vinegar, olive oil and thyme leaves. Blitz until completely smooth. Transfer to a bowl and add lemon juice and black pepper, to taste.
Serve warm or at room temperature with the prepared crudites. The dip will keep for a couple of days covered in the fridge. You can warm it back up for dipping or use it to dress pasta.