In a large bowl, whisk together the flour, sugar, salt, and dry yeast.
Pour the warm milk into the dry ingredients, then add the egg, melted butter, vanilla extract, and honey.
Mix the ingredients until combined, 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 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 about 340°F (170°C). Test the oil by dropping in one doughnut; if it immediately rises to the surface and bubbles gently, 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.
Once the doughnuts have cooled slightly, drizzle them with honey, or make a honey glaze by mixing powdered sugar with honey.
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