For the fat chips, heat the oil in a deep-fat fryer to 140C/285F. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Slice the potatoes into 1.5cm/½in thick chips.
Place the chips into the hot oil to cook for 5-6 minutes, until just tender but not coloured. Remove from the oil with a slotted spoon and set aside.
Increase the temperature of the oil to 190C/375F.
Return the chips to the hot oil and cook for 3-4 minutes, until golden-brown and cooked through. Remove with a slotted spoon and drain on kitchen paper. Season with salt.
Keep the oil hot. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
For the 'scampi', place the egg yolks, flour, salt and freshly ground black pepper in a bowl and whisk together.
Add the beer and whisk to a smooth batter.
Place the egg whites into a separate bowl and whisk until stiff peaks form when the whisk is removed.
Add half of the egg whites to the batter and mix well, then carefully fold in the remaining egg whites.
Dip the monkfish cheeks into the batter to coat thoroughly, then place into the hot oil in batches and cook for 2-3 minutes, until golden-brown and cooked through. Remove from the oil with a slotted spoon and drain on kitchen paper.
For the tartare sauce, place the egg yolks, vinegar, mustard, salt and lemon juice into a food processor and blend to combine.
With the food processor still running, gradually add the rapeseed oil, until all the oil has been added and the tartare sauce has thickened.
Spoon the mixture into a bowl, then add the remaining ingredients and mix well. Season to taste with salt and freshly ground black pepper.
To serve, place equal amounts of the fried monkfish and chips onto each plate and serve with a dollop of tartare sauce alongside.
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James Martin presents a compilation of favourite Saturday Kitchen moments.