Place the flour, spices, sugar and salt in the bowl of a stand mixer. Briefly mix together. Add the yeast, the 1 tbsp of vegetable oil, egg, milk and water. Using the stand mixer fitted with the dough hook, knead the dough for 6-8 minutes until smooth and elastic.
Pour a little extra oil into the bowl, lift up the dough and then flip it over to coat with oil. Cover with a damp cloth and leave somewhere warm until doubled in volume.
Tip the risen dough out onto a work surface dusted with flour. Punch it down and then roll it out to be able 5mm (1/4-inch) thick. Using a 7cm (3-inch) round cutter or glass, stamp out circles of dough. Use the back end of a pastry tip to cut out circles from the centre of the dough. Re-roll the scraps and cut out remaining doughnuts.
Place the cut doughnuts onto a baking sheet dusted with flour. Cover with a damp cloth and leave somewhere warm for 30 minutes to rise again.
Heat about a 3cm (1-inch) depth of vegetable oil in a deep frying pan to 180oC (350oF).
Gently lower the doughnuts into the oil, a few at a time, and let fry until golden underneath. Flip and fry on the other side until golden. This will only take 1-2 minutes on each side. Remove to a baking tray lined with paper towels to drain excess oil.