For the aïoli, place the yolk in a mixing bowl along with the mustard, garlic and vinegar. Begin whisking and slowly add the oils to emulsify with the yolk. As the oils incorporate into the yolk, you can speed up the process.
When all the oil has been added, season with salt and pepper and add some lemon juice and vinegar to taste. Set aside.
For the chorizo-stuffed squid, pull the tentacles away from the body of each squid and reserve them. Check the centre of the tentacles for the hard beak, which can be discarded. Feel inside the body for the quill of each squid (it resembles a shard of plastic). Pull it out of the squid and discard. Rinse inside the body in cold water. Pull the ears (wing-like flaps) from the body. Pull the purplish skin from the ears and body to leave only the white meat.
Discard the guts of the squid or, if desired, retain the ink sack to use in seafood pasta or risotto.
Knead the chorizo in a bowl together using your hands to form a rough paste. Take a piece of chorizo and form it into a shape to fill the cavity of one of the squid.
Fill each squid to about two-thirds full and press it down. Secure each squid tube with a cocktail stick and reserve until ready to cook.
Cook the potatoes in a pan of salted water until tender and then drain well. Heat a non-stick frying pan over a medium heat, add a lug of olive oil, the crushed garlic and the potatoes and season well with salt and freshly ground black pepper. Cook over a moderate heat tossing occasionally to evenly crisp and caramelise the potatoes.
Take another non-stick pan and place over a moderate heat. Season the squid pockets and tentacles with salt and pepper. Add a lug of oil to the pan and add the squid. Cook for two minutes on one side and then turn over and cook for a further two minutes.
Add the butter and sage and, when foaming, spoon it over the squid to cook further and ensure the chorizo is cooked inside. The filling will feel firm to the touch when cooked.
Add the peas, capers and zest and remove the pan from the heat. When the potatoes are ready, transfer to a plate lined with kitchen paper to drain.
To serve, divide the potatoes between serving plates along with the squid, the buttery pan juices, peas, capers and zest. Serve with a dollop of aioli.