Preheat the oven to 350 degrees. Season the lamb with salt and pepper. Place the lamb leg in a roasting pan and add the butter, rosemary sprigs, 8 garlic cloves, 1 cup olive oil, and 1 cup white wine. Cover with foil and cook for 35 minutes. Remove the foil and cook for another 15- 20 minutes turning the lamb leg often.
Meanwhile, remove the outside leaves of the artichokes and then peel the surrounding stem. Cut the artichokes in half stem-side up. Place the artichokes into a container of water with lemon. (This helps reduce the oxidation of the artichokes turning black.) Place the artichokes in a pan face down. Add the sea salt, ½ cup extra-virgin olive oil, wine, vegetable stock, anchovies, 3 cloves crushed garlic, 8 mint leaves. Simmer on a medium flame until cooked.
Serve the lamb with the artichoke mixture.