In a deep-fryer or heavy-bottomed pot, heat enough peanut oil to come halfway up the sides of the pot, to 325 degrees F.
In a large and shallow dish, whisk together the coconut milk, egg, grated ginger and flour to form a thick batter. To a second shallow dish, add in the shredded coconut. Dip the prawns in the batter, then roll them thoroughly in the coconut shreds. Drop them, in batches, into the peanut oil and fry until their exteriors are golden brown and crisp, about 4 to 5 minutes. Transfer them from the fryer to a platter lined with paper towels and immediately season them with salt and black pepper. Transfer the prawns to a serving platter and sprinkle with cilantro and lime juice. Serve them with the dipping sauce.
In a small saucepan over medium heat, warm the mango chutney over low heat. Add the coconut milk and stir well to combine. Stir in the zest, lime juice, sugar, cayenne, ginger and salt. Continue cooking until the ingredients are fully incorporated and the sauce has warmed through. Add some chopped cilantro and remove the saucepan from the heat. Transfer the sauce to a serving bowl and serve with the Ginger and Coconut Crusted Jumbo Shrimp.