Boil the quails’ eggs in a pan of boiling salted water for 2½ minutes, drain and place in a bowl of iced water for a couple of minutes, drain again and peel.
In a bowl mix the crab with the egg yolk, tarragon, salt and pepper.
Wrap this mixture around the quails’ eggs squeezing the crab gently around the egg until completely covered.
Prepare three plates: one with plan flour, another with the beaten egg, and another with the panko breadcrumbs.
Dip the quails’ eggs into first the flour, then the egg wash and finally into the breadcrumbs, using a teaspoon to help coat the egg with each layer.
Fill a deep-sided pan up to a third with sunflower oil and heat to 160C/325F. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Place the eggs carefully into the oil using a metal spoon and cook for about three minutes, or until golden-brown, then take the eggs out and drain on a plate lined with kitchen paper.