Warm the milk slightly, crumble in the yeast, add a teaspoon of sugar, and let it stand for 10 minutes until foamy.
In a large bowl, whisk together the flour, remaining sugar, and salt.
Pour in the proofed yeast mixture, melted butter, and eggs. Start kneading the dough.
Knead the dough thoroughly for 10 minutes until smooth and elastic. If necessary, add a little more flour or milk to achieve the right consistency.
Cover with a kitchen towel and let rise in a warm place for about 1 hour, or until doubled in size.
On a lightly floured surface, roll out the dough to about 1 cm (½ inch) thickness. Use a glass or doughnut cutter to cut out circles.
Let the doughnuts rise for another 30 minutes to make them even lighter during frying.
In a deep skillet or pot, heat the oil to 340-355°F (170-180°C). Fry only a few doughnuts at a time to keep the oil temperature stable.
Fry the doughnuts for 2-3 minutes per side, until golden brown. Remove them to a paper towel-lined plate to drain excess oil.
Prepare the Baileys cream: heat the heavy cream, then stir in the Baileys Irish Cream Liqueur and melted dark chocolate until smooth.
Fill the cooled doughnuts with the Baileys cream using a pastry bag.
Dust the doughnuts with powdered sugar and serve fresh to fully enjoy the liqueur-infused cream.
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