In a large bowl, whisk together the flour, cocoa powder, sugar, salt, and dry yeast.
Pour the warm milk into the dry ingredients, then add the egg, melted butter, and vanilla extract.
Mix the ingredients together, then knead the dough for 8-10 minutes until it becomes smooth and elastic.
Cover the dough 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 dough to about 1 cm (½ inch) thickness. Use a glass or doughnut cutter to cut out circles.
Place the cut-out doughnuts on a baking sheet lined with parchment paper, and cover with a clean kitchen towel. Let them rise for another 30 minutes.
In a large pot, heat the oil to approximately 340°F (170°C). Test the oil by dropping in a doughnut: if it immediately rises to the surface and gently sizzles, the oil is ready.
Fry the doughnuts for 1-2 minutes per side, until golden brown and slightly crispy. Use a slotted spoon to remove them, then place them on paper towels to drain excess oil.
Once the doughnuts have cooled slightly, prepare the creamy filling: whip the heavy cream until stiff peaks form, then fold in the mascarpone cheese and powdered sugar until light and fluffy.
Cut the doughnuts in half, and fill with the mascarpone cream. Gently replace the tops.
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