Butter an oven proof baking dish well with some of the butter.
Soak the salted salmon in water (or alternatively in milk for at least 4 hours, to draw out the salt. Remove the salmon from the liquid, and remove the skin and pat dry very well with a kitchen towel. Slice thin into approximately 5 cm (about 2 inch) slices.
Boil the potatoes in salt water until soft but still firm, drain and let them cool. Peel after cooling and slice into the same thickness as the salmon. Sautee the sliced onions over low in the remaining butter until soft, without coloration.
Layer the onions, salmon and potatoes into the baking dish starting with the potatoes, sprinkling each layer generously with the chopped dill and freshly ground white pepper from the mill. Finish the top with another layer of potato slices.
In a bowl, beat the eggs lightly then add the cream and lightly season the mixture with salt. Pour the mixture over the layered potatoes and salmon until just covered and add a few morsels of butter on top.
Bake in a preheated oven at 160 °C ( 320 °F) for approximately 45 minutes or until the Lax pudding is baked through, the egg mixture has set and has a golden brown crust over the top.