This is an attempt to emulate the high heat stir fry techniques restaurants achieve with burners that are just slightly cooler than the sun. You don't have this (I don't think) so a bit of extra work is a necessary evil here.
Combine all the sauce ingredients in a small bowl. Set aside.
Prep your beef. If using sirloin a small roast (or baseball steak) works well. Put the sirloin in the freezer for about 20 minutes and then slice about as think as you can get (1/8") across the grain. If you are using flank or skirt slice on the vertical bias (so the slice is bigger than the steak is high).
Use a wok for this if you can. It's just easier. A big frying pan will do as well. Pre-heat it over medium high heat. Add 2 tablespoon of the oil.
Turn the heat up to high. Crank it. When the oil starts to shimmer (that should happen fast) add half of the beef. Half is important. You don't want to overload your pan. You'll get steam if you do that and your beef won't brown. Cook, tossing frequently, until it gets some colour. Remove.
Add the remaining tablespoon of oil. Add the remaining beef and cook you did with the first half. Set aside.
Turn the heat down to medium. If your wok looks dry at this point add a bit more oil. Add the onions and cook until they are well softened.
Turn up the heat. Add the broccolini and stir fry until it starts to soften. Be vigorous. Toss stuff around. Like you were on TV. Have fun with it. This takes a couple minutes or more depending on how high your heat is.
You want to try to get a bit of that charred flavour on the broccolini. Push it hard. Your onions will start to really shrink and darken. Like fried shallots. That's good. After about two minutes if the onions are getting too dark add a couple tablespoons of water to the wok to cook things down a bit.
Turn the heat down to medium and add the garlic ginger paste. Cook for about 30 seconds, then add the beef back into the wok.
Add the sauce and toss until everything is warmed through. Add the cornstarch-water mixture and simmer until the sauce just starts to cling to the broccolini. Taste. If you think it isn't salty enough let it cook another minute to concentrate the flavours a bit. Remove from heat. Add the red chilies if using.
Garnish with sesame seeds and serve with jasmine rice.