Rinse and dry the slices of beef, for example, using kitchen paper towels. If the beef slice has a tough tendon around the edges, cut it off.
Cut the beef slices around the circumference, roughly one notch by 2 inches (notch depth no more than ¼ inch). It's not as complicated as it may sound; just make a vertical cut with a knife or meat cleaver.
Tenderize the slices and lightly salt and pepper them. Dredge each piece of meat on both sides in flour. Lightly shake off the excess flour from the meat.
Peel and finely chop the onion.
In a pot wide enough to fit all the beef slices side by side, heat the oil over medium to high heat. Sear the meat on both sides until golden brown. Each side will need about 1-2 minutes.
Transfer the seared beef to a plate and set aside.
Turn the heat down to medium, add the chopped onion. Using a flat wooden spoon, scrape the browned remains from the bottom of the pan, stirring the onions as you do so.
Add a tablespoon or two of water and continue to work carefully with a flat spoon. The browned residues from the bottom will dissolve in the liquid. Stir until the onions are golden brown.
Put the beef slices back into the onion base, including any juices released from the meat. Pour in water so that the meat is submerged to about half its height. Stir and salt and pepper the base if necessary.
Cover the pan with a lid, bring to a boil. Then reduce the temperature to a minimum and let it simmer gently until the meat is tender. The softening time depends on the type and age of the beef used (see cooking tips below).
Once the meat is soft, it is time to make the gravy. Transfer the beef slices to a plate and keep them warm. Pour the liquid through a sieve and use a spoon to strain the remaining onion into the juice. If necessary, add some salt for better taste.
Now arrange the slices of beef on a plate, pour the finished gravy over them and serve with a suitable side dish.