Bone the saddle of lamb, separating the two loins.
For the purée, peel the garlic, cook it for 15 minutes in the milk. Strain and discard the milk. Purée the garlic.
Roughly crush the hazelnuts. Combine the garlic purée with the hazelnuts.
Pick the leaves from the basil, peel and finely chop the French shallots. Lay out the two halves of the saddle, skin side down.