Combine lime juice, olive oil and salt and pepper in a large bowl. Add prawns, toss well to coat, and marinate in fridge for about 1 hour.
Meanwhile make the mayonnaise, using either an electric whisk or a hand whisk. Sit a medium-sized mixing bowl on a damp cloth to stop it moving.
Put egg yolks and mustard in the bowl and season well. Pour a drop of oil onto the eggs and blend. Repeat, then continue to add the oil, drop by drop, until the mixture starts to thicken and becomes pale and glossy. Then you can add the oil faster in a thin, steady stream.
When all the oil has been incorporated, stir in the tequila and the parsley.
Taste the mayonnaise and adjust seasoning if necessary.
Preheat the barbecue or chargrill pan to high.
Remove the prawns from marinade and cook each side for about 3 minutes, or until they turn pink and are cooked through.