For the Sauce:
1 egg yolk
½ cup extra-virgin olive oil, plus more for drizzling
1 whole salt-packed anchovy, soaked, drained and filleted in half (optional)
Juice from ½ a lemon
1 tablespoon Dijon mustard
1 teaspoon capers
1 tablespoon water
Salt, to taste
For the Carpaccio:
1½ pounds lamb top round, trimmed of all fat, sinew and gristle, and cut into ¼-inch slices, chilled
1 small shallot, very thinly sliced
¼ cup finely chopped green olives, preferably lucques olives
6 figs, halved and thinly sliced
¼ cup loosely packed tarragon leaves
¼ cup loosely packed mint leaves, thinly sliced
Zest from 1 lemon
Pinch of Marash pepper or cayenne pepper
Fleur de sel
1. Make the sauce: Add the egg yolk to a blender. With the motor running on high speed, begin adding the oil a few drops at a time. Once the mixture begins to thicken, add the rest of the oil in a slow stream. Add the anchovy, lemon juice, mustard and capers and continue to process until you have a smooth sauce. Transfer to a small bowl and whisk in the water. Season with salt. Set aside until ready to use.
Note: The aioli can be made the day before; cover it with plastic wrap and refrigerate. Bring it to room temperature before serving.
2. Make the carpaccio: Place one piece of lamb in between two pieces of parchment paper. Using the flat side of a mallet or a small heavy bottomed pot, gently pound the meat into ⅛-inch thickness. Remove the top parchment paper and invert the lamb onto a chilled plate. Refrigerate for at least 30 minutes.
3. To serve, arrange the meat in a single layer around the plate, then drizzle some of the sauce over each piece. Top with the shallots, green olives, figs, tarragon, mint and lemon zest. Sprinkle with pepper and fleur de sel and drizzle with olive oil. Serve immediately.