Place a rack in middle of oven; preheat to 275°F.

If lamb is tied or trussed, remove any twine or netting.

Sprinkle lamb all over with 3 Tbsp. sumac, 5 tsp. Diamond Crystal or 1 Tbsp. Morton kosher salt, and 1 Tbsp. pepper.

Reroll lamb so the fattier side is on top.

Using 3–4 pieces of kitchen twine, tie lamb in 2" intervals to close.

Place bottom halves of both garlic heads, cut side up, in the center of a 13x9" baking dish and set lamb, fat side up, on top.

Scatter cloves from remaining top halves of garlic heads around lamb, then tuck artichokes and sprigs from ½ bunch oregano around.

Pour in wine and oil; season vegetables with salt and pepper.

Roast lamb and artichokes until a thermometer inserted into the thickest part of lamb registers 135°F for medium-rare, 2–2 ½ hours.

Remove lamb and artichokes from oven and increase temperature to 500°F.

Once oven temperature is at 500°F, 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, 10–12 minutes.

Carefully transfer lamb to a cutting board and let rest at least 20 minutes.

Meanwhile, scatter half of mint leaves over artichokes and toss well to coat.

Toss radishes, shallot, and vinegar in a small bowl to combine; season radish salad with salt and pepper.

Thinly slice lamb and arrange on a platter or serve directly on cutting board and spoon some of the artichoke mixture and any pan juices over.

Scatter sesame seeds, oregano leaves, more sumac, and remaining mint on top.

Spoon some aioli into a bowl and serve lamb with radish salad, aioli, and remaining artichoke mixture alongside.

Do Ahead: Lamb and artichokes can be roasted 3 hours ahead. Let sit at room temperature. Reheat artichokes just before serving.