Step 1: Prepare the Pickle-Brined Carrots (Optional, but Highly Recommended). In a small jar or container, combine the ½ cup of dill pickle brine and the 1 cup of sliced carrots. Make sure the carrots are submerged. Let them sit at room temperature for at least 30 minutes, or refrigerate for up to a few hours. This will give them a quick-pickle effect.

Step 2: Season and Brown the Lamb. Season the lamb shoulder chops generously with salt and freshly ground black pepper. Heat the vegetable oil in a large heavy skillet or Dutch oven over high heat. Working in batches, brown the lamb chops on both sides, about 3-5 minutes per side. Transfer the browned lamb to your stock pot.

Step 3: Sauté the Onions. Reduce the heat to medium. Add the chopped onion and a pinch of salt to the same skillet (there should be some rendered lamb fat left in the pan). Cook and stir until the onions are softened and slightly browned, about 5 minutes.

Step 4: Make the Roux. Stir in the butter until melted. Add the flour and stir constantly until the onions are evenly coated, about 1 minute.

Step 5: Deglaze and Thicken. Gradually pour in the chicken stock, stirring constantly to prevent lumps. Add the dried rosemary. Bring the mixture to a boil, stirring until it thickens, about 5-10 minutes.

Step 6: Combine and Simmer. Pour the thickened stock mixture over the lamb in the stock pot. Add the chopped carrots (the ones not being pickled), celery, and the finely chopped pickled onions. Add water as needed to ensure the meat is completely submerged. Bring the mixture to a simmer, then reduce the heat to low, cover the pot, and cook until the meat is almost falling off the bone, about 1 ½ hours.

Step 7: Add Potatoes. Remove the lamb from the stew and set it aside on a plate. Add the baby Dutch yellow potatoes to the stew. Return the lamb to the pot, placing it on top of the potatoes.

Step 8: Continue Simmering. Cover the pot and continue to simmer until the potatoes are tender and the meat is completely falling off the bone, about 30 minutes more.

Step 9: Reduce the Sauce (Optional). Remove the meat and potatoes with a slotted spoon and set them aside. If you want a thicker sauce, bring the stew to a boil and cook, skimming off any excess fat, until it reaches your desired consistency, about 10-12 minutes.

Step 10: Shred the Meat. Remove the meat from the bones and discard the bones and any large pieces of fat. Shred the meat with two forks or your fingers.

Step 11: Return Meat to Stew. Stir the shredded lamb back into the stew. Add the green onions. Season with additional salt and pepper to taste. Add the drained, pickle-brined carrots.

Step 12: Serve. Ladle the stew into bowls. Serve hot, with chilled dill pickle spears on the side. Encourage your guests to add a pickle spear or two to their bowl, or to enjoy them alongside the stew.