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1
Adjust oven rack to lower position and preheat oven to 300u00b0F (150u00b0C). In a small bowl, combine brown sugar, salt, garam masala, paprika, turmeric, ground ginger, onion powder, garlic powder, cumin, and cayenne pepper. If lamb is tied up, remove twine and unfurl on a work surface. Season lamb all over with 2 to 3 tablespoons spice mixture, making sure to rub it on all sides. Reserve remaining spice mixture.
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2
Using butcher's twine, tie up lamb shoulder into an even cylinder.
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3
In a medium bowl, whisk together ketchup, tomato paste, Worcestershire, Dijon, molasses, cider vinegar, liquid smoke, hot sauce, and fish sauce. Stir in 1/4 cup of reserved spice mixture. Season with salt, if necessary.
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4
Heat oil in a Dutch oven over medium-high heat until shimmering. Add lamb and cook, turning occasionally, until well browned on all sides, about 5 minutes total. (Lamb will brown fast because of the sugar; do not let it burn.) Add onion and cook, stirring and scraping up browned bits from the bottom of the pan, until softened, about 2 minutes.
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5
Add half of sauce mixture and chicken stock to Dutch oven, stirring to blend; reserve remaining sauce. Cover, transfer to oven, and cook until lamb is just starting to turn tender, about 2 hours. Remove lid and continue cooking until a knife or fork shows very little resistance when twisted inside the meat and a dark bark has formed, about 1 hour longer; add a small dose of water if at any point the pot goes dry during the last hour.
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6
In a large bowl, combine cabbage, carrot, parsley, cider vinegar, mayonnaise, caraway, and mustard seeds, tossing to combine thoroughly. Season with salt and pepper.
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7
Transfer lamb to a large bowl, reserving liquid in pot. Using a ladle, skim off excess fat from liquid and discard. Add reserved sauce to pot and whisk to combine. When lamb is cool enough to handle, shred with two forks.
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8
Ladle sauce into lamb, tossing until meat is nicely coated; you may not need to add all the sauce. Season to taste with more salt, sugar, liquid smoke, or cider vinegar, as desired.
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9
Pile pulled lamb onto the bottom half of each bun. If you have extra sauce, you can ladle some onto each pile of lamb; you can also lightly sprinkle with any remaining spice rub. Top with slaw, close buns, and serve.
