Preheat your oven to 220° C (430° F).
In a small bowl, mix together olive oil, garlic, salt, pepper, and dried thyme (or oregano).
Slit the top of the fatty side of the lamb shoulder joint with a small sharp knife to help the marinade go through the meat.
Rub the mixture all over the lamb, gently massaging it into the meat for a couple of minutes.
Wrap the lamb shoulder tightly with 2 layers of large pieces of parchment paper followed by 2 layers of tin foil.
Place the wrapped lamb shoulder on a cooking rack sitting on a baking tray, then place it in the preheated oven.
Cook the lamb for 2 ½ hours, and then reduce the heat to 140° C (285° F).
Let the lamb cook for another 2-3 hours, until it is fork-tender.
Remove the lamb from the oven, place it in a large bowl or plate, and carefully open the wrappings.
Separate the meat from the bone using a thong or a fork, shred it, and transfer it to a baking dish along with the cooking juices.
Set the oven temperature to 180° C (360° F), and place the lamb meat back in the oven for 15 to 20 minutes, until the meat lightly browns.
Place the naan bread or pita bread in the oven for 10 minutes to warm them up before serving them with your Kuzu Tandir Kebab.