Trim the lean central part of the lamb away from the bones and fat. Season it with salt and pepper.
In a large ovenproof skillet or roasting pan over medium-high heat, heat the olive oil with the garlic cloves until the garlic browns a little and becomes fragrant. Brown the lamb all over, then put the pan into the preheated oven.
While the lamb is roasting, make the sauce. Combine all the sauce ingredients except the eggs and butter in a small saucepan. Cook over low heat until almost all the liquid has been absorbed or evaporated. Set aside.
In a metal bowl set in a saucepan of gently boiling water, whisk the egg yolks until they change to a pale yellow color. Add the butter to the eggs, a little at a time, whisking constantly. When the sauce is fluffy, add the mushroom mixture to the sauce. Keep warm.
When the lamb is done to your liking remove it from the oven and let it rest for 15 minutes. When ready to serve, slice the noisettes about 3/4 inch thick. Serve two slices per person with the sauce spooned generously over the top.