Warm the milk slightly and stir in one teaspoon of sugar. Crumble in the yeast and let it stand for 5-10 minutes until foamy.
Sift the flour into a large bowl, add the sugar and salt, and mix. Crack in the eggs, pour in the proofed yeast, melted butter, and rum.
Knead the dough thoroughly until it is soft and elastic. If necessary, add a little flour to prevent it from being too sticky.
Cover the dough with a kitchen towel and let it rise in a warm place for about 1 hour, or until doubled in size.
On a lightly floured surface, roll out the risen dough to about 1 cm thickness. Use a glass or cookie cutter to cut out circular shapes.
Place the dough pieces on a floured baking sheet, cover, and let them rise for another 20-30 minutes.
Heat the oil in a deep skillet over medium heat. Fry the doughnuts until golden brown on both sides (about 2-3 minutes per side).
Remove the fried Krofne to a paper towel-lined plate to drain excess oil, then dust with powdered sugar or fill with jam and serve.
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