In a large bowl, combine the flour, granulated sugar, salt, and active 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 elastic and smooth.
Cover the dough and let it rise in a warm place for about 1 hour, or until it has doubled in size.
On a lightly floured surface, roll out the dough to about 1 cm 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 an additional 30 minutes.
In a large pot, heat the oil to about 340°F (170°C). Test the oil by dropping in one doughnut; if it immediately floats to the surface and gently sizzles, the oil is ready.
Fry the doughnuts for 1-2 minutes per side, until golden brown. Use a slotted spoon to remove them and place them on paper towels to drain excess oil.
Prepare the sugar cream filling: in a saucepan over medium heat, combine the heavy cream, brown sugar, butter, and cornstarch. Cook, stirring constantly, until thickened.
Once the doughnuts have cooled slightly, use a pastry bag to fill them with the cream.
Sprinkle the tops of the doughnuts with powdered sugar and a pinch of cinnamon for the perfect flavor.
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