Preheat the oven to 325°F. Have on hand an oven-safe dutch oven or casserole dish to cook the lamb in.
In a large enough pan to hold the lamb, heat the olive oil.
Add the diced shallot and garlic and cook for a few minutes.
Rub the lamb with the salt, pepper, and rosemary.
Place the lamb in the pan and sear on each side until brown turning often.
Transfer the lamb and all of the garlic and shallot to the casserole dish.
Add the beer, broth, thyme, and carrots to the lamb.
Place in the oven covered with a lid or foil and cook for 2 hours turning the lamb over once or twice.
After 2 hours take the lid off and cook for another hour.
Turn the temperature up to 400 degrees and continue to cook the lamb until it feels fork tender.
Once the lamb is done transfer it to a plate and cover loosely with foil.
Skim all of the fat from the dish and discard along with the carrots and thyme sprigs.
Transfer the remains to a pan and add 2 tbsp flour.
Whisk the flour into the liquid and gradually add the broth until simmering and the gravy has become thinner.
Once the gravy is done pass it through a sieve and transfer to a gravy dish. Shred the lamb into chunks and serve with potatoes and gravy on the side.
*Note* Depending on the size of your lamb, cooking time may vary. The real test will be when you test it with two forks and it pulls apart.