I have never been certain, on whatever coastline, of the difference between shrimp and prawns. My heritage is the eastern coast, so I think of shrimp as small and prawns as large—probably an unfounded assumption. In this case, use whatever fresh shrimp or prawns you can find.
Put the shrimp in a pot and cover with
Stir salt and pepper to taste into the lime juice and then whisk in the olive oil. Peel the shrimp and put them in the lime juice mixture. Save the shrimp shells, put them in a food processor, and grind them up. Sieve the shells, pressing out all the liquid. Add the reserved liquid to the marinade and discard the shell debris.
Divide the mayonnaise into thirds. Mix the basil into one part, the chopped cilantro into another, and the pepper puree into the remaining part.
Cut the avocados in half, remove the pits, and scoop out each half with a spoon. Cut each half crosswise into ⅛-inch slices. Push gently down and across on each avocado half to make a fan; then lift each half onto a plate. Put the shrimp in the inside curve of the avocado and pour the shrimp marinade over all. Garnish with the cilantro sprigs and serve with the 3 mayonnaises.
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