How to Make It
In a small saucepan, combine the unseasoned rice vinegar with 1/2 cup of sugar, 1 cup of water, the mustard seeds, peppercorns, star anise, clove and 2 tablespoons of sea salt. Bring the pickling liquid to a boil. Put the ripe papaya in a heatproof bowl and pour the hot pickling liquid over it. Let stand for 1 hour, until cool.
Meanwhile, in a large saucepan, combine the remaining 1 1/2 cups of sugar with the remaining 3 cups of water and the mint sprigs and bring to a boil, stirring until the sugar dissolves. Add the green papaya and cook over moderate heat until tender, about 45 minutes. Strain the papaya and let cool slightly; discard the mint. Transfer the cooked papaya to a blender and puree until smooth. Transfer to a bowl and refrigerate until cold.
In a small skillet, toast the coriander seeds, fennel seeds, whole cloves, allspice berries and star anise pod over moderate heat, shaking the pan until fragrant, about 2 minutes. Transfer the toasted spices to a plate to cool.
Heat the vegetable oil in a medium saucepan. Add the chopped carrot, celery, onion, ginger and lemongrass and cook over moderate heat, stirring, until the vegetables are softened, about 7 minutes. Add the toasted spices and the wine to the saucepan and cook over moderately high heat until the wine has evaporated, about 5 minutes. Add the coconut milk, 6 lime zest strips, basil and cilantro and bring to a boil. Cover and let stand off the heat for 30 minutes. Strain the coconut broth through a fine sieve set over a medium bowl, pressing hard on the solids with the back of a spoon to extract as much liquid as possible. Refrigerate the coconut broth until well chilled.
Drain the pickled papaya and pick out the peppercorns, star anise and cloves; pat the papaya dry. Add the green papaya puree, lime juice and cold water to the coconut broth; season with salt and hot sauce. Ladle the papaya soup into shallow bowls, mound the pickled papaya in the center of each bowl and arrange the lobster on top. Garnish the papaya soup with lime zest and serve at once.