How to Make It
Make the pickles Put the daikon in a heatproof medium bowl. In a medium saucepan, bring the remaining ingredients to a simmer, stirring to dissolve the sugar. Pour the hot brine over the daikon and let cool slightly. Cover and refrigerate for at least 2 hours.
Meanwhile, make the sauce In a small saucepan, combine all of the ingredients and cook over moderately low heat, stirring occasionally, until thickened slightly, about 30 minutes. Let cool slightly. Transfer to a blender and puree until smooth. Transfer to a small bowl, cover and refrigerate until chilled, about 1 hour.
Make the shrimp Prepare an ice bath. In a large saucepan, combine the garlic, lemongrass, jalapeño, bay leaf, lime leaf, salt and spices with 8 cups of water and bring to a boil. Reduce the heat to moderately low, add the shrimp and simmer until just cooked through, about 7 minutes. Drain and transfer the shrimp to the ice bath. Let cool completely. Drain, peel and devein the shrimp, leaving the tail end intact; discard the shells and aromatics.
Serve the shrimp with the drained pickled daikon, cocktail sauce, shrimp chips and basil.
Shrimp chips, a fried cracker, can be found at Asian groceries and on amazon.com.