For the burger and fries, put the mince in a large bowl and season with salt and pepper. Use your hands to shape the mince into four burger-shaped patties. Wrap the patties individually in cling film and place in the fridge for an hour.
Meanwhile, for the tomato chutney, heat the oil in a small pan. Add the shallot, tomatoes and garlic and cook for 5-8 minutes until softened. Add the vinegar and sugar and cook for 3-5 minutes until the chutney has caramelised slightly.
For the truffle mayonnaise, put the egg yolks, mustard and a pinch of salt and pepper in a food processor and combine. Mix the oils in a jug, then, with the motor running, slowly pour oil through the feed tube until you have a thick emulsion. Mix in the lemon juice and a little warm water to loosen, if necessary.
The mayonnaise will keep for up to 2 days in the fridge. Just before serving, stir in the truffle shavings.
When you are ready to cook the burger and fries, heat the vegetable oil in a deep-fat fryer to 190C. Alternatively, heat the oil in a deep saucepan until a cube of bread sizzles and turns brown when dropped in. (CAUTION: Hot oil can be dangerous; do not leave unattended.)
Carefully add the potatoes to the fryer and cook for 2-3 minutes, or until just coloured and crisp. Remove from the pan using a slotted spoon and set aside to drain on a plate lined with kitchen paper. Season with salt.
Heat a large frying pan with a little oil. Cook the burgers on each side for 2-3 minutes, or until cooked to your liking (you can serve the burger rare as you are using fresh steak mince).
To serve, put each burger in a brioche roll topped with the gherkins, tomato slices, chutney, lettuce, a few onion slices and the truffle mayonnaise. Secure with a wooden skewer and serve with the fries.