For the fish fingers, place the vegetable oil into a deep, heavy-based saucepan and heat until a small cube of bread sizzles and turns golden-brown when dropped into it, or preheat a deep fat fryer to 190C/375F. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Place the egg yolks, flour, salt and freshly ground black pepper into a bowl and whisk together.
Pour in the beer and whisk to make a smooth batter.
Place the egg whites into a separate bowl and whisk until stiff peaks form when the whisk is removed.
Beat half the whisked egg whites into the batter, then gently fold in the remaining half.
Dip each piece of fish into the batter to coat thoroughly, shaking off any excess.
Carefully place the fish into the hot oil in batches and deep fry for 3-4 minutes, or until golden-brown and cooked through. Remove from the oil with a slotted spoon and drain on kitchen paper.
Once all the fish is cooked, drop several pieces at a time back into the oil for 30-45 seconds - this helps to make them really crisp. Remove from the oil with a slotted spoon and drain on kitchen paper.
Meanwhile, for the pea purée, heat the butter in a pan and gently fry the shallots for 1-2 minutes.
Add the peas and warm through gently, then add the cream and mint leaves and cook for a further minute.
Transfer the mixture to a food processor and blend to a purée. Season, to taste, with salt and freshly ground black pepper and add a squeeze of lemon juice.
For the parsley oil, place the parsley and olive oil into a small food processor and blend to a purée. Pour the mixture into a sieve lined with muslin or a clean kitchen cloth and leave to drip into a bowl.
To serve, spoon the pea purée onto four serving plates and top with some pea shoots. Place three fish fingers onto each plate and drizzle over the parsley oil.