Heat a large heavy pot over medium-high heat and add Ghee. Sear the Mutton, bone-in in batches until well browned on all sides; transfer the browned pieces to a plate and set aside.
Reduce heat to medium, add a little more ghee if needed and sauté the chopped Yellow onion until translucent. Add minced Garlic and grated Fresh ginger and cook until fragrant, about 1–2 minutes.
While the aromatics cook, dry-toast the Coriander seeds, Cumin seeds, Fennel seeds and Black peppercorns in a small skillet over medium heat until fragrant and slightly darkened, then crush coarsely with a mortar and pestle or spice grinder.
Add the whole spices—Cinnamon stick, Star anise, Whole cloves and Green cardamom pods—to the pot with the onions and briefly fry to bloom their aroma, about 30–60 seconds. Stir in the toasted crushed seed mix.
Return the browned mutton to the pot and pour in enough Water to cover the meat by an inch or two. Stir in the Rock sugar and bring to a gentle boil, skimming any foam from the surface. Reduce to a low simmer, cover partially, and cook until the mutton is tender, about 1.5–2 hours depending on the cut.
About 30–40 minutes before the end of cooking, add the peeled and chunked Potatoes, sliced Carrots, chopped Tomatoes and sliced Celery. Continue to simmer until the vegetables are tender and the flavors have melded.
Season the soup with Salt and freshly ground White pepper to taste; adjust sweetness with a touch more rock sugar if desired. Remove any large whole spices (like cinnamon or star anise) if you prefer before serving.
Ladle the soup into bowls and garnish with Fried shallots, chopped Fresh coriander (cilantro) and sliced Spring onions (scallions). Serve immediately with a wedge of Lime to squeeze over each bowl for a bright finish.
