Preheat oven to 375˚F.
Place garlic, anchovies, anchovy oil, and black pepper in a small bowl and whisk together.
Lightly season lamb chops with salt and pepper.
Brush garlic-anchovy mixture over each chop, on both sides.
Pour olive oil into a large sauté pan and place over medium-high heat.
Sear each chop in the pan for 2 to 3 minutes, on each side, and transfer to a roasting pan.
Roast lamb chops for about 13 to 15 minutes for medium-rare, and 15 to 18 minutes for medium doneness. Remove from the oven and allow chops to rest for 5 to 7 minutes.
Using the same pan you used to sear the chops, melt the butter over medium-low heat. Allow butter to cook for 6 to 8 minutes or until butter has melted and begins to foam and brown. Add olives and sage leaves and gently fry for 1 to 2 minutes. Remove mixture from the heat. Season with salt and pepper.
Transfer chops onto a serving dish/platter and pour butter sauce over chops. Serve immediately.