I am pretty particular when it comes to eating and cooking liver. I only like it when its interior is pink—like meat, like eggs, the liver continues cook after you turn off the stove, and so catching the liver at just the right moment is of the utmost importance.
There is nothing (nothing!) that makes me grumpier and more prone to tears in the kitchen than overcooking liver. Liver, when cooked rare to medium rare, is so sweet and creamy, you could eat the leftovers cold, like pâté. But overcooked liver is so disappointing, so grainy and tough. (The last time I cooked liver for too long, it was in a very hot wok and I was distracted by a phone call, and in a blink of an eye, my liver had turned a smidgeon more grey than pink. It was very upsetting. I had to stop what I was doing and put my head down for a minute.)
For stir-fried liver, timing is everything. The pieces of liver are already cut into smaller segments, so keeping the interior rosy-pink can be more of a challenge. Now, I always err on the side of caution by cutting into the liver as I'm stir-frying it, just to make sure it's not overcooked. (Kenji recommended doing the same thing with steak - that is to say, if you don't have a meat thermometer, it's better to cut into the sucker rather than risk a tough and overdone steak. Something about that piece of advice seemed so liberating to me, maybe because no one wants to admit that it's what he or she does secretly does, anyway.)
Depending on what I'm in the mood for, I make the liver sweet and savory with oyster sauce, or spicy and salty with fermented chili bean paste. (Oyster sauce, by the way, is easily one of my favorite condiments. It doesn't taste especially like oysters, but it is packed with a concentrated and briny flavor.) I like both versions about the same; oyster sauce highlights liver's inherent sweetness, while chili bean paste brings out out liver's iron-like flavors.
Finally, a note on authenticity: I feel that stir-fried liver is not a dish for which it is advisable to scrimp on the oil. More oil means the liver stays tender on the inside, all the while getting nice and brown on the exterior, in no time at all.
So if I were in China, or cooking this dish for my Chinese relatives, I would put down quite a lot of oil (about one cup) in my wok, and stir-fry the livers until they were not even close to being cooked through. Then I would get rid of the excess oil in the wok, add the seasonings, and stir-fry for a little while longer to finish cooking the dish. (That technique, by the way, is called "passing through the oil" in Chinese cookery, and it is very frequently used for meat as well as vegetable dishes.) If you like, you can use the "passing through the oil" method and cut down on the cooking time.
But stir-fried liver and onions is very good with less oil, stir-fried in the usual way. Only a few tablespoons of oil are called for in the recipe.
Personally, I like to think of how much additional iron I'm getting in my diet, which, in a just and ideal world, would somehow make up for the fat.