For the prawns, preheat a deep-fat fryer to 180C/350F.
Cook the vermicelli in boiling water for 2-3 minutes, or until just softened. Drain and refresh in iced water, then drain once more. Pat dry with kitchen paper and mix with a little of the olive oil.
Wrap each prawn in a basil leaf, then wrap with 4-5 vermicelli strands.
Carefully lower the prawns into the deep-fat fryer and cook for 2-3 minutes, or until the prawn is cooked through and the pasta is crisp and golden-brown. Repeat with the remaining prawns.
Remove the prawns from the deep-fat fryer, set aside to drain on kitchen paper and season with a little salt and freshly ground black pepper.
For the lemon basil mayonnaise, blend the lemon zest, basil leaves, egg yolks, vinegar and mustard in a food processor until smooth. While the motor is still running, slowly add the oil until the mixture has emulsified and all of the oil has been added. Season with the lemon juice, salt and freshly ground black pepper.
To serve, spoon the mayonnaise into the centre of the serving plates. Place three prawns onto each plate, then scatter over the remaining basil leaves and drizzle with olive oil.