1. Preheat the oven to 450°. On a large rimmed baking sheet, separate the sliced shallot into rings and toss with the oil. Spread the shallots on the baking sheet and bake for 10 minutes, stirring once, until most of the rings are deeply browned. Transfer to a medium bowl.
2. Meanwhile, in a medium skillet, toast the coconut over moderately high heat, stirring, until lightly browned, about 2 minutes. Transfer to the bowl with the shallots and wipe out the skillet. Add the sesame seeds and toast over moderately high heat, shaking the pan, until golden, about 30 seconds. Transfer to the bowl with the shallots and coconut. Stir in the basil, ginger and chiles.
3. Add the coconut milk to the skillet; bring to a boil over moderately high heat. Add the shrimp and simmer, stirring, until just cooked through, about 3 minutes. Stir in the lemon juice. Season with salt and pepper. Spoon the shrimp into bowls, top with the shallot and sesame seed sprinkle and serve.
Serve With: Steamed rice.
Notes: Variations: The shallot, basil and sesame seed sprinkle can be served over Asian noodles or grilled pork chops or used as a garnish for curries.