For the lime sherbet, in a saucepan, whisk together the milk and sugar over a medium flame, until the sugar is dissolved.
Remove the mixture from heat and cool over an ice bath. Stir in the lime juice, and then process in an ice cream machine according to the manufacturer's instructions.
For the dressing, combine the mango puree, asafetida, salt, and sugar in a bowl and whisk together until mixed. While whisking slowly drizzle in the oil, and continuing to whisk until an emulsification is reached.
For the salad, slice the mango thinly or use a peeler and peel the flesh into long strips.
Toss the mango strips, mache, pistachios, and crystallized ginger with the dressing, and then arrange in a small mound on the plate. On top, set a scoop of the lime sherbet.
Begin by gently peeling the skin from two lobes of ginger. Using a knife or peeler tends to remove too much flesh; a less wasteful method is to use the edge of a spoon.
Slice both lobes lengthwise into thin pieces, using a mandoline or knife.
Add 2 cups water and 2 cups of the sugar to a medium saucepan, and bring to a boil over high heat. Reduce the heat, add the ginger, and simmer for 20 to 30 minutes, or until they are soft.
Remove the ginger pieces using a strainer and cool briefly.
Spread the remaining 4 cups of sugar on a baking sheet and dredge the ginger pieces in the sugar until both sides are entirely covered.
Transfer the ginger to another baking sheet and air dry for several hours, until crisp. Cut into short, 2-inch sticks. Place in an airtight container. They will last for more than 3 months.