In a mixing bowl place bread flour, sugar, instant yeast and salt. Mix with a wire whisk to incorporate all ingredients.
Add warm milk/water, egg and vegetable oil then mix with a spatula until rough dough forms. Fix mixing bowl in the mixer with dough hook attachment and beat at low-medium setting for 12 minutes or until dough is smooth, elastic and doesn't break when pulled.
Grease clean counter top or flat surface with a bit of oil and place dough on top to avoid dough sticking. Knead for a couple of seconds then shape it into a ball.
Transfer in another bowl and coat with thin layer of oil so it will not dry out while rising. Let it rise for 1 hour or until double in size. While resting prepare/cut 16 pcs. of 12 cm X 12 cm parchment paper. Set aside.
When dough doubled in size you know you achieved a good rise. Lightly press on the dough to release the air/gas inside. Dump the dough on a lightly dusted flour counter top and flatten with a rolling pin approx. ½ cm thick.
Use a 9 cm diameter cookie cutter to cut circles in the dough. Re-roll the scraps then shape again with the cookie cutter. Place each donut in the prepared parchment paper.
Arrange in a baking pan and cover with a kitchen towel to rest for 30 minutes or when it doubles in size.
Heat oil over medium heat in a heavy bottomed pot until it reaches 375°F/190°C. Add 2-3 doughnuts at a time and cook for 1 minute on each side. Carefully remove with a metal spatula or metal slotted spoon and transfer in cooling rack. Repeat process with remaining doughnuts.