Cut the sole fillets in half lengthways, and then slice each fillet half into about 4 long strips on the diagonal. This will give you 8 goujons from each fillet.
Put the cornstarch into a shallow bowl and season with salt and pepper. Put the bread crumbs or panko into another shallow bowl, and beat the eggs together in an additional bowl.
Dip each goujon into the seasoned cornstarch, coating it well, then the beaten egg, and finally the bread crumbs.
Lay the goujons on a cooling rack for a while, and heat the oil in a pan. (Or at this point you can freeze them in layers of baking parchment in an airtight container.)
Fry the goujons for about 2 minutes, or until crisp and golden. Remove to pieces of kitchen towel, as you go, to remove excess oil.
For the Dill Mayonnaise:
Put the mayonnaise into a bowl, and finely chop the dill, adding it to the mayonnaise. Stir in some lime juice and taste for seasoning. Serve with the prepared fish.