Start by brining (salting) the cod with coarse salt for 15 minutes.
Rinse the cod free of salt and dry the cod in a tea towel.
Season with salt and pepper.
Heat a pan to medium-high heat and add butter and oil. When the butter has melted, place the cod on the pan with the skin side down.
Let the cod cook until the heat has reached the middle of the fish. Then turn the cod, reduce to medium heat and cook for an additional 3 minutes.
Peel the celeriac and Jerusalem artichokes and cut them into smaller pieces - about 2 x 2 centimeters to reduce the cooking time.
Boil them until tender. This takes about 20 minutes.
Put the boiled pieces of Jerusalem artichokes and celeriac in a good blender with half a deciliter cream / milk and blend to a smooth purée. If you prefer a thinner purée, add a bit more liquid.
Season with salt, pepper, and lemon.
Peel the Jerusalem artichokes and slice them on a mandolin (about 1 - 1.5 millimeters thick)
Pat them dry with a tea towel.
Heat the oil in a pan.
Fry the Jerusalem artichokes in the oil until there are no more bubbles around them. They should preferably be light in the middle. Do not overcrowd the pan.
Let the fried chips drain on absorbent paper and sprinkle with salt.