In a small bowl, combine the salt, black pepper, smoked paprika, garlic powder, ground cumin, dried rosemary, and dried thyme. Rub the olive oil all over the lamb shanks, then coat them evenly with the spice mixture. Let the seasoned shanks sit at room temperature for 20 minutes.
Preheat the air fryer to 400 degrees F. Place the lamb shanks in the basket and sear them at 400 degrees F for 8 minutes, turning halfway through, until they are deeply browned on all sides. This initial sear builds incredible flavor.
While the shanks sear, whisk together the beef broth, red wine, and tomato paste in a bowl.
Tear off two large sheets of heavy-duty aluminum foil. Place one lamb shank on each sheet. Divide the smashed garlic, chopped onion, and fresh rosemary sprigs between the two packets. Pour half of the broth mixture over each shank.
Wrap the foil tightly around each shank, crimping and sealing all edges so no liquid can escape. The sealed packets create the steam needed to braise the meat to tenderness. Place the foil packets in the air fryer basket. Cook at 325 degrees F for 1 hour and 15 minutes.
Carefully open one packet and check the meat. It should be very tender and pulling away from the bone. If it is not falling-off-the-bone tender yet, reseal the foil and cook for an additional 15 to 20 minutes.
Once the shanks are tender, open the foil packets and carefully transfer the lamb shanks back to the air fryer basket, discarding the foil. Spoon a little of the braising liquid over the top. Increase the heat to 400 degrees F and cook uncovered for 4 to 5 minutes to caramelize the exterior.
Serve the lamb shanks with the strained braising juices spooned over the top. These pair wonderfully with creamy mashed potatoes or polenta.