Make the ice block a day ahead with water in a mold. Rinse the potatoes and put them in a pot with salted water. Boil them for 10 minutes, remove from heat and let them absorb the warm water until serving.
Take the herring out of the brine and let them drip dry on a paper towel, then place them on the block of ice.
Put the warm potatoes on plates, add dabs of butter and sprinkle with chopped dill. Last of all, season with some sea salt and fresh ground pepper and drip on a little aquavit.
Eat the herring and potatoes with rye bread and butter.