For the celeriac remoulade, place the egg yolks, mustards and vinegar into the bowl of a food processor and blend until well combined.
With the motor still running, gradually add the sunflower oil in a thin stream, until the mixture thickens and becomes smooth and glossy. (If the mayonnaise starts to thicken too quickly, loosen it with the tiniest drop of warm water, then continue.)
Add the olive oil in the same way, until the mixture is creamy in texture. Taste and add a drop or two more vinegar, if necessary. Season to taste with salt.
Peel the celeriac, then slice to a 1mm thickness using a mandolin or very sharp knife. Pile the celeriac slices on top of each other, then cut the slices into thin strips using a sharp knife. Work as quickly as possible to prevent the celeriac from discolouring. Alternatively, grate the celeriac.
Mix the celeriac with the dill in a large mixing bowl, then add enough mayonnaise to bind it together. Set aside for 30 minutes.
Meanwhile, for the chips, rinse the potato fries under cold water, then drain well and pat dry using kitchen paper. Dry as thoroughly as possible.
Heat the oil in a deep-fat fryer to 140C/285F. Alternatively, heat the oil in a deep-sided, heavy-based pan until a breadcrumb sizzles and turns golden-brown when dropped into it. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
When the oil is hot, add the chips (in batches if necessary) and fry for three minutes. Remove from the pan using a slotted spoon and set aside to drain in a colander lined with kitchen paper.
Increase the heat to 180C/350F, then return the chips to the hot oil and fry for five minutes, or until lightly golden-brown. Remove from the oil again and drain in the colander (lined with fresh pieces of kitchen paper). Season with salt and keep warm.
For the venison burger, season the venison mince with salt and freshly ground black pepper. Shape the seasoned mince into four thick burgers. Rub each burger all over with a little olive oil.
Heat a griddle pan over a medium to high heat. When the pan is smoking, add the burgers and cook for 3-4 minutes on each side (for medium), or until brown griddle marks have appeared on the outside of the burgers and the burgers are cooked to your liking.
To serve, place each burger into a bread roll and top with red onion, gherkins and a dollop of ketchup, if desired. Place the burgers onto four plates. Serve the chips and celeriac remoulade alongside.