Preheat oven to 450 F. You will need a roasting pan with a tight-fitting lid that is large enough to fit the lamb shanks in one layer.
Place lamb in roasting pan and rub both sides of shanks with olive oil. Season both sides generously with salt and pepper.
Roast for 20 minutes, uncovered. Lamb will be a nice brown colour. Take the lamb out of the oven and turn the oven down to 325 F.
Remove excess fat from bottom of roasting pan. Pierce the skin of the garlic cloves with the tip of a knife. Place the garlic cloves in the pan around the lamb shanks. Place 1 rosemary sprig on each lamb shank. Place remaining rosemary sprigs in the pan around the lamb shanks.
Once oven temperature has dropped to 325 F, add the lid to the roasting pan and return lamb shanks to oven.
Roast the lamb for 2 hours. Do not check on the lamb or remove the lid because you will increase the risk of making the meat too tough. Trust me on this!
Once the 2 hours are up, remove the lamb from the oven. Remove the lid and add the broth you are using to the pan.
Turn oven up to 400 F and return lamb (uncovered) to oven for 10 minutes.
Remove lamb from oven. Place shank on plate. Spoon over the juices from the pan.
Pop roasted garlic out of their skins. Spread on lamb or eat whole - either way is delicious!