Heat a heavy-based frying pan over a high heat and add the olive oil and butter. Add the venison to the pan and fry, turning regularly, until browned all over.
Place the meat onto a trivet in a roasting tin and roast in the oven for about five minutes. Remove from the oven and set aside in a warm place to rest.
Meanwhile, heat another frying pan over a medium heat, add the hazelnut oil followed by the finely chopped shallot and fry until the shallot is softened but not coloured.
Increase the heat (add a splash more hazelnut oil if necessary) and when the pan is hot, add in the chanterelles and tarragon and fry for 1-2 minutes. Remove the pan from the heat, season with salt and freshly ground black pepper.
Meanwhile, reheat the venison jus until piping hot, check the seasoning and add the elderberries. Toast the brioche slices.
Place a slice of toasted brioche onto each plate, carve the venison and place onto the brioche. Spoon over the jus and then generously scatter over the chanterelles.