To make the avocado salad, peel and coarsely grate the unripe avocados into a bowl. The unripe avocados should be hard, such that when being grated will sound like grating carrot.
Whisk together the lime juice, fish sauce, palm sugar and chilies. Taste and adjust the ingredients to obtain the harmony of hot, sour, salty and sweet. Pour over grated avocado and toss well. Cover and leave for 15 minutes.
To make the avocado prawn filling, put chestnuts, firm-ripe avocado, coriander and tomatoes in a bowl and toss. Spoon equal quantities of prawn mixture into each lettuce cup and top with a generous amount of avocado salad. Garnish with shallots and sprigs of coriander.
To serve as a roll up, substitute the lettuce cups for softened rice paper rolls.