Cut each sole or lemon sole fillet into strips, on the diagonal, about 1cm/½ in thick. Mix the breadcrumbs with the cayenne pepper and leave to one side. Heat the oil in a deep fat fryer to 190C/375F.
Season the flour with salt and pepper. Coat the fish in the seasoned flour, then dip first in the beaten egg and then in the breadcrumbs. Do a few pieces at a time, making sure all the fish is coated in each of the three dips.
Place a few of the goujons in the fryer at a time and cook for about one minute, until crisp and golden brown. Repeat until all the goujons are cooked. Once cooked, remove on to some kitchen paper to soak up the excess oil.
Pile the goujons in a dish or on plates, season, and serve with the lemon wedges. They're great with a mixed, dressed green leaf salad.
For the mushy peas, soak the peas in a large bowl, in three times their volume of water with the bicarbonate of soda for at least four hours or, if you have the time, overnight.
Drain the peas, rinse under the tap, and place on the stove in a large pan and cover with the water. Cover and bring to the boil and once boiled, reduce the heat and simmer the peas for 1½-2 hours, stirring from time to time.
The peas should be soft and mushy in texture but not too dry. If they are wet, continue cooking over the heat with the lid off to dry out a little. Beat in the butter and season.
Serve the mushy peas with the fish, sprinkle with a little cayenne pepper and top with a lemon wedge.