Set up a food processor and, with the motor running, drop in the clove of garlic and process until minced.

Add yolk, mustard and lemon juice to the bowl of the food processor and pulse several times to combine the ingredients.

With the machine running, add the oil through the feed tube in a very slow, thin stream.

Before all the oil is added, periodically stop the machine to check the consistency to be sure it is not too thick. It should end up with the consistency of mayonnaise.

Stir in the lemon zest and the tarragon, and season with salt and pepper to taste. Keep refrigerated for up to a week.

To make the fritters, coarsely chop half of the shrimp and set the other half in a food processor.

Add the egg white, cream, shallot, salt and pepper to the food processor. Process until light and fluffy, about 2 minutes. Transfer the mixture to a bowl and stir in the chopped shrimp. Gently fold in chopped herbs. Cover and chill for 10 minutes.

Place the breadcrumbs in a pie plate or shallow dish. Drop the shrimp mixture by heaping tablespoonfuls onto the crumbs, then gently roll in the crumbs and shape the mounds into balls. Transfer to a parchment-lined sheet tray.

Heat 1/4-inch of oil in a heavy, shallow pan over medium heat until hot but not smoking. Fry the fritters until golden on the bottom. Flip and continue to fry until golden brown and firm to the touch, about 4 minutes total.

Drain the fritters on a rack set over a sheet tray.

Transfer to a platter, and serve with the aioli.