This is the model recipe for making stir-fried chicken with firm vegetables, those that must be parboiled before stir-frying. The extra step sometimes saves time and always helps you pinpoint doneness. But if you want to cook everything in one pan, cut the broccoli into small bits (1/2 inch or so) and start the recipe at Step 2. Serve with white or brown rice.
Add the rice to a small saucepan and rinse until the water is no longer cloudy. Add enough water to cover the rice by 1 inch and add a pinch of salt. Bring to a boil over high heat, then simmer until "craters" form in the rice, about 10 minutes. Lower the heat all the way and cover until ready to serve.
Bring a large pot of water to a boil, salt it and cook the broccoli until it just loses its rawness, 8 to 10 minutes. Drain, then run under cold water to stop the cooking. Chop into bite-size pieces.
Put a large skillet over high heat. Add 2 tablespoons oil, swirl it around and immediately add the onions, ginger and garlic and cook until the onion begins to brown and the garlic is fragrant, about 5 minutes. Remove the onion mixture to a plate. Add 1 tablespoon oil to the pan, then add the broccoli in an even layer and cook until it begins to brown, tossing occasionally, 3 to 5 minutes. Remove the broccoli to the plate with the onion mixture.
Add the remaining 1 tablespoon oil to the pan, then add the chicken. Raise the heat to high, stir the chicken once, and let it sit for 1 minute before stirring again. Continue cooking, stirring occasionally, until the chicken has lost its pink color, 3 to 5 minutes.
Return the vegetables to the pan and toss once or twice. Add the soy sauce and scallions and toss again. Sprinkle with salt and pepper, then add the stock and cook, stirring and scraping the bottom of the pan, until the liquid is reduced slightly and you've scraped up all the bits of chicken, about 30 seconds. Garnish with more scallions and serve over the rice.