For the tartar sauce: Make a mayonnaise by mixing the vinegar, Dijon and egg yolks to a paste in a medium bowl. Slowly add the vegetable oil in a thin stream, whisking all the time. When emulsified, mix in the capers, gherkins, parsley, shallots and hard-boiled eggs. Set aside.
For the pea puree: Bring the chicken stock just to the boil in a small pan.
Put the butter in a medium pan, add the shallots and 1/2 teaspoon sea salt and gently fry. Add the peas and sugar, then pour in the chicken stock. Bring to the boil and cook until the peas are tender. Strain, reserving the cooking liquid.
Transfer the peas and shallots to a blender, and add the mint and a few tablespoons of the cooking liquid. Blend to a puree, adding more cooking liquid as required. Season with salt and pepper. Keep warm.
For the chips: Top and tail the potatoes and cut into chips using an apple slicer/corer (alternatively cut into chunky wedges).
Bring a pan of salted water to the boil and blanch the chips until soft but still holding their shape. Remove the chips with a slotted spoon and drain them on a perforated tray (alternatively use plates lined with paper towels).
Fill a deep-fat fryer or heavy pot with vegetable oil and heat until a deep-fry thermometer inserted in the oil registers 284 degrees F. (Caution: Hot oil can be dangerous. Do not leave unattended.)
Cook the chips, in batches if necessary, until the oil stops bubbling (which means that the moisture has been removed), 8 to 10 minutes. Remove the chips using a slotted spoon and drain on a perforated tray or plates lined with paper towels.
For the battered fish: Beat the egg whites in a bowl until very soft peaks form when the whisk is removed. In a separate bowl, mix the flour, baking soda and sparkling water together. Stir in the egg white mixture. Mix to just combine, but don't over work (a few lumps are fine). Set aside to rest for 20 minutes.
Heat the oil in the deep-fat fryer to 350 degrees F. Deep-fry the chips for a second time until crisp and golden-brown.
Meanwhile, sprinkle some flour onto a shallow plate. Dust the fish pieces with the flour, dip in the batter and deep-fry until the batter is golden-brown and crisp (you may need to do this in batches).
Season the chips with salt and serve immediately with the fish, pea puree and tartar sauce.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.