"Lamb, a classic springtime meat, stars in this comforting dish that's perfect for the chilly, dreary days between winter and spring. Garnish with sliced green onions. Breaking up the cooking time yields a superior texture and flavor but you can also cook the lamb all at once, simmering until fork-tender for 2 1/2 to 3 hours."
Heat olive oil in a deep-sided pan or pot over medium-high heat. Add lamb and cook, turning as needed, until browned, about 5 minutes. Remove from pan and reduce heat to medium.
Place chopped onion, carrot, celery, and garlic in the pan. Season with a large pinch of salt. Cook and stir until vegetable juices start to come out, about 2 minutes. Add tomato paste and stir to coat, about 1 minute. Pour in beer and stir in rosemary. Raise heat to high and bring sauce mixture to a simmer.
Toss lamb shanks in with the sauce mixture. Reduce heat to low. Cover and simmer until lamb is nearly fork-tender, flipping lamb after 1 hour, about 2 hours. Remove from heat and let cool to room temperature, at least 30 minutes. Refrigerate, 8 hours to overnight.
Skim the fat off the top of the sauce, if desired. Cover and bring lamb to a simmer over low heat. Flip and continue simmering until meat is fork-tender and nearly falling off the bone, about 45 minutes. Place lamb shanks in a bowl to keep warm.
Bring sauce to a boil over high heat. Boil until reduced by half but not too thick, about 3 minutes. Season with salt and cayenne pepper. Plate the lamb shanks and spoon sauce on top.