Place a rack in the middle of the oven; preheat to 275°. If lamb is tied or trussed, remove any twine or netting and sprinkle the lamb all over with Mediterranean seasoning, kosher salt and pepper. Pat the mixture into the lamb so it adheres.
Truss the lamb with the fattier side on top. Using 3–4 pieces of kitchen twine, tie lamb in 2" intervals to close. Place bottom halves of both garlic heads and all the halved shallots, cut side up, in the center of a 13x9" baking dish and set lamb, fat side up, on top of the garlic and shallots. Scatter the remaining garlic cloves around the lamb, along with the artichokes and oregano sprigs. Pour in wine (or stock if you don’t cook with wine) and oil and season vegetables with salt and pepper. Roast lamb and artichokes until a thermometer inserted into the thickest part of lamb registers 135° for medium-rare, 2–2½ hours.
Remove the lamb and artichokes from oven and increase temperature to 500°. Once oven temperature is at 500°, slide baking dish back into oven and roast until fat on lamb is golden brown and artichokes are sizzling and starting to crisp around the edges, about 10 minutes. Carefully transfer lamb to a cutting board and let rest for at least 30 minutes
Thinly slice lamb and arrange on a platter or serve directly on a cutting board and spoon some of the artichoke mixture and any pan juices over. Scatter the oregano leaves, mint leaves, lemon juice and zest on top. Serve immediately.