Rub lamb cutlets with olive oil, then press garlic, thyme, rosemary and bay leaves into the lamb flesh. Marinate overnight, then discard herbs and garlic.
Roast lamb bones at 200C for about 40 minutes, turning once, or until well browned on both sides.
Heat oil in a large, heavy-based saucepan over medium heat. Add carrot, celery and onion, cook for about 10 minutes, or until translucent, stirring frequently.
Add roasted lamb bones to pan, with wine, stock, garlic and bouquet garni. Bring to a boil, skimming well, then reduce heat and gently simmer for about 2 hours.
Strain sauce through a fine-mesh sieve into another saucepan and reduce over very low heat until measuring about 350ml – this will take about 2 hours. Strain through muslin cloth into a clean saucepan and set aside.
Preheat oven to 180C. Season lamb with salt and pepper. Place an ovenproof pan on the stove top over a high flame. Seal lamb pieces on both sides, then place in oven. Roast until core temperature reaches 58°C when checked with a thermometer (about 10-15 minutes). Remove from oven, cover with foil and allow to rest for about 10 minutes.
Heat the sauce and stir in olives, capers, anchovies and vinegar. Plate each lamb cutlet with generous spoonfuls of the sauce, garnish with fresh thyme.