In a medium saucepan, combine the coconut milk, lime juice, fish sauce, soy sauce, palm sugar, ginger, lemongrass, chilli and makrut lime leaves. Bring to a boil over medium-high heat, then reduce to a gentle simmer.
Add the chicken breast, ensuring it is fully submerged. Poach gently for 12–15 minutes, or until the chicken is just cooked through.
Remove the chicken from the poaching liquid and transfer to the fridge to cool completely. Reserve ½ cup of the poaching liquid and refrigerate until chilled.
Once the chicken is cool, shred or slice to your desired texture.
In a large bowl, combine the iceberg lettuce, mint, coriander, bean sprouts, spring onions, lychees and thinly sliced makrut lime leaves. Add the chicken and chilled poaching liquid, then toss to combine.
Divide between serving bowls and top with crushed peanuts and fried shallots. Serve immediately.