Cut the pointy tips from each chicken wing and discard. Dry the wings well on kitchen paper.
Heat the oil for deep-frying to 180C/350F (use a cooking thermometer), or alternatively use a deep fat fryer. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Deep fry a quarter of the chicken wings for 6-7 minutes, until cooked through, crisp and golden-brown.
Meanwhile, for the dressing, put the garlic cloves on a board, sprinkle with some salt and crush them into a smooth paste with the flat side of a large knife.
Put the extra virgin olive oil and the crushed garlic in a small pan over a medium-low heat. As soon as the garlic begins to sizzle, add the crushed dried chillies and cook very gently for two minutes, until the garlic is very lightly golden-brown.
Stir in the sweet paprika and sherry vinegar and remove from the heat.
As soon as the first batch of chicken wings is cooked, remove them from the oil with a slotted spoon and drain them briefly on kitchen paper. Tip them into a serving bowl and drizzle with some of the warm garlic and chilli dressing.
Stir to coat the chicken with the dressing then sprinkle with a little sea salt.
Repeat with the remaining wings frying in batches.
For the peas, heat the olive oil in a medium, lidded, frying pan. Add the shallots and garlic, cover and cook gently for five minutes until soft but not browned.
Stir in the peas and chicken stock, part-cover and simmer gently for five minutes until the peas are tender and the liquid has reduced to leave them just moist.
Stir in the Serrano ham, and season to taste with salt and pepper.
Break the eggs, spaced well apart, on top of the peas, season lightly with salt and freshly ground black pepper and cover the pan with a well-fitting lid.
Leave to cook gently for five minutes, or until the eggs are set to your liking.
To serve, pile the hot chicken wings alongside the peas and eggs.