Preheat oven to 325°F. Place shredded coconut on a sheet pan and toast in oven for about 15 minutes or until golden brown, stirring every few minutes. Trim the ginger and cut into thin slices, then cut the slices into thin matchsticks. Save any scraps or trimmings. Cut one lime into wedges.
Place the chicken breast, ginger trimmings, coconut milk and salt in a medium saucepan. If necessary, add enough water to cover the chicken breast. Place over high heat and bring to a boil, reduce heat and let simmer 7 minutes, turning the chicken breasts halfway through. Once internal temperature of chicken is at least 165°F, remove from heat and let cool to room temperature. Shred the chicken and save the liquid.
While the chicken is cooking, chop the peanuts, slice the cucumber and wash and cut the lettuce into wedges, 6-8 per head. Pick the leaves from the mint and cilantro.
Take ½ cup of the liquid from the poached chicken and stir in sugar and the juice of one lime. Adjust with more lime and salt to your liking. Toss the shredded chicken with ¼ cup of this dressing.
Arrange the lettuce wedges and cucumbers on serving plates, top with the shredded chicken, then the herbs, julienned ginger, toasted coconut and chopped peanuts. Spoon more of the dressing over all. Serve with lime wedges.
Approximate Nutritional Information (Per serving):
Calories 590, Fat 39g, Sat. Fat 26g, Trans Fat 0g, Cholesterol 80mg, Sodium 660mg, Total Carbohydrate 29g, Fiber 7g, Sugars 11g, Protein 39g
ALLERGEN INFORMATION: Egg-Free, Soy-Free, Dairy-Free