How to Make It
In a medium saucepan, combine the sugar with both vinegars, the salt and 1/2 cup of water. Bring to a boil, stirring to dissolve the sugar. Remove from the heat and add the mushrooms, kaffir lime leaves and thyme and let stand until cooled completely. Transfer to a jar, cover and refrigerate until chilled, about 30 minutes.
In a large enameled cast-iron casserole, heat the oil until shimmering. Add the onion, garlic, ginger, lemongrass and kaffir lime leaves and cook over moderate heat, stirring occasionally, until softened and just starting to brown, about 8 minutes. Add the squash and red curry paste and cook, stirring, until the squash is coated and just starting to soften, about 10 minutes. Add the stock, coconut milk and 2 cups of water and bring to a boil. Simmer over moderately low heat, stirring occasionally, until the squash is very tender, about 25 minutes.
In batches, carefully puree the soup in a blender and transfer to a heatproof bowl. Strain the soup through a fine sieve back into the casserole and bring just to a simmer. Season with salt and pepper and keep warm.
In a large skillet, heat the oil until shimmering. Add the garlic and ginger and cook over moderately high heat, stirring, until fragrant, about 30 seconds. Add the bok choy and cook, tossing, until just wilted and crisp-tender, 2 to 3 minutes. Remove from the heat and season with salt and pepper.
Ladle the soup into shallow bowls, top with the bok choy and some of the pickled mushrooms and serve.
Kaffir lime leaves are the fragrant leaves of kaffir limes, a fruit native to Indonesia, Thailand and other parts of Southeast Asia. They are available at Southeast Asian and some Asian markets and online at importfood.com.