For the duck burger, roughly remove about two-thirds of the fat from each duck breast and then chop them into chunks and pass through a mincer. Season the meat well and form into two balls using your hands.
Take one ball of meat and push a scoop of Vacherin into the centre. Form the meat around the Vacherin and pat down a little to make a classic burger shape. Repeat with the remaining ball and scoop of cheese.
Preheat the oil in a deep fat fryer to 160C/325F (CAUTION: hot oil can be dangerous: Do not leave unattended.)
Rinse the chipped potatoes under cold running water to remove any excess starch. Dry thoroughly on a clean tea towel and then place into the hot oil to cook for about 8-10 minutes. The chips should begin to lightly colour on the outside and be soft enough to crush between your fingers.
Carefully remove the chips from the oil with a slotted spoon and drain on a plate lined with kitchen paper. Increase the oil temperature to 180C/350F
In the meantime, heat a griddle pan over a high heat. Once hot, add the burgers and fry for 3-4 minutes on each side until nicely cooked on each side and just cooked through in the middle. If you like your burger fully cooked through, place in a hot oven for a few minutes to finish. Otherwise, place the burgers on to a plate to rest.
Place the sliced shallots onto the hot griddle to caramelise. Cook for about two minutes.
Heat the butter in a separate pan over a high heat. Add the mushrooms and fry for 3-4 minutes, or until just softened.
When you are ready to eat, add the chips to the hot oil and cook for 2-3 minutes, or until golden-brown and crisp. Remove and drain on a plate lined with kitchen paper.
Serve the duck burgers with the shallots and mushrooms in a brioche bun.