Season the lamb with salt and pepper. In a large, heavy Dutch oven, heat 3 tablespoons of the oil. Add the lamb and cook over moderately high heat until browned, 12 minutes; using a slotted spoon, transfer to a plate.
Add the shallots, anchovies, rosemary and most of the garlic to the Dutch oven and cook over moderate heat, stirring, until the shallots are softened, 5 minutes. Stir in the potatoes and cook just until browned in spots, 2 minutes. Add the rosé and cook until nearly evaporated, scraping up any browned bits, 5 minutes. Add the lamb and any accumulated juices, the olives and 2 cups of water and bring to a boil. Cover and simmer over moderately low heat until the lamb is tender and the potatoes are cooked through, 50 minutes.
In a bowl, mash the remaining minced garlic to a paste. Stir in the chopped basil and the remaining 2 tablespoons of olive oil. Stir the mixture into the stew and serve.