To make the sauce, soak the dried shrimp in hot water for 15 minutes. Meanwhile, trim and discard the leafy parts of the lemongrass stalk, remove the tough outer leaves from the bulb until the smooth, pale green core is exposed, and trim off the root end.
Starting from the root end, cut the bulb crosswise into paper-thin slices, stopping when you reach the point where the purple rings disappear. Set the slices aside and discard the remainder.
Place the dried coconut flakes in a wok or a 14-inch (35 cm) skillet and toast them over medium heat, stirring constantly, until they are medium brown, about 2 to 3 minutes. Reserve 2 tablespoons of the toasted coconut flakes for the sauce and set the remainder aside for the salad. Wipe out any toasted coconut residue from the wok.
Add the lemongrass slices, shallot, galangal, and ginger to the clean wok. Toast over medium-high heat, stirring constantly, until fragrant and the shallot slices feel dry to the touch, about 5 minutes. Transfer the toasted mixture, drained dried shrimp, and shrimp paste to a mortar or mini chopper, and grind to a smooth paste.
Place the prepared paste, sugars, fish sauce, and water in a 1-quart saucepan, and bring to a boil over medium-high heat, stirring constantly. Once the sauce has thickened and reduced to about 1 cup, after 2 to 3 minutes, remove the saucepan from the heat and let the sauce cool completely. When the dressing has cooled, stir in the chopped peanuts and the reserved 2 tablespoons of toasted coconut flakes, then transfer it to a small serving bowl.
To prepare the salad, quarter the lime lengthwise and trim away the core. Cut the quarters into 1/4-inch (5 mm) dice, leaving the rind intact. Alternatively, for those sensitive to the bitterness of the lime rind, cut the lime into wedges and allow diners to squeeze about 1/2 teaspoon of lime juice onto each composed salad bite.
Arrange the lime, ginger, shallots, peanuts, chiles, dried shrimp, cha phlu leaves, and dressing on a large serving platter.
To eat, place a leaf in your palm, add a bit of each component to the center of the leaf, top with a small spoonful of dressing, gather the corners of the leaf to form a bag, and eat the whole thing in one bite.