In a stand mixer bowl, combine the lukewarm milk and sprinkle the yeast over it. Allow it to sit undisturbed for 5 minutes, then stir gently. Incorporate the sugar, vegetable oil, egg, orange zest, and vanilla, whisking until unified.

Gradually add the flour along with the pinch of salt. Using the dough hook attachment, mix the dough at low speed (not exceeding speed 2) until a cohesive dough forms. Continue kneading with the machine for approximately 7 minutes, ensuring a smooth and elastic consistency.

Transfer the dough to a clean surface and knead briefly. Shape into a ball and place into a lightly oiled bowl, turning the dough to coat all sides. Cover with plastic wrap and allow it to rise in a warm, draft-free environment until tripled in volume, roughly 2 to 3 hours.

Once risen, deflate the dough gently and roll out to a thickness of ¼ to ⅓ inch. Use a 2½ inch (6½ cm) round cutter to shape six donuts. Arrange them on a baking sheet lined with parchment, cover again with plastic wrap, and leave to rise for an additional hour.

Heat approximately 2 inches of vegetable oil in a medium saucepan to a steady 340–350°F (170–175°C). Maintain this temperature range while frying. Cook the doughnuts in batches, turning occasionally, for about 2–3 minutes per side until golden.

Remove with a slotted spoon and briefly place on a paper towel-lined plate. Immediately roll the hot donuts in granulated sugar, ensuring full coverage.

Allow the donuts to cool slightly. Using the handle of a wooden spoon, create a cavity on the side or top of each donut. Enlarge the opening gently and fill with your preferred pastry cream, chantilly, or hazelnut spread. Serve immediately for best results.