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 Balsamic 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.
Feta Rice Pilaf With Orzo
2 Tablespoons Butter
1/2 Cup Orzo Pasta
1/2 Cup Diced Onion
2 Cloves Garlic, Minced
1/2 Cup White Rice
2 Cups Chicken Broth
1 Cup Chopped Spinach
1/2 Cup Chopped Bulgarian Feta Cheese
Melt butter in a skillet over medium-low heat; cook and stir orzo in the melted butter until golden brown, 3 to 5 minutes. Stir onion into orzo and cook until translucent, 5 to 10 minutes. Cook and stir garlic into orzo-onion mixture until fragrant, about 1 minute.
Mix rice and chicken broth into orzo-onion mixture; bring to a boil. Reduce heat to medium-low, cover skillet, and simmer until rice is tender and liquid is absorbed, 20 to 25 minutes. Remove from heat and stir in spinach and feta. Cover and let stand until spinach is wilted and feta is melted, about 5 minutes. Fluff with a fork.