Place the Chinese broccoli in a colander. Run them in water to wash off any dirt. Dry with a paper towel. Cut the hard bottom part of the stem. Then cut the stems off the leaves. Use a vegetable peeler or a knife to peel the outer layer of the stems. Set aside.
For the sauce, combine soy sauce, oyster sauce, and sesame oil, stir to mix well. Set aside
Heat the oil into a small saucepan. Add the garlic, cook until they turn slightly brown. (remove from the heat as soon as you see them changing color, the garlic will continue to cook as they sit). Use a heat-proof bowl and strain the garlic. Transfer the garlic onto a paper towel to drain excess oil. Set aside.
Boil water into a larger soup pot, and add salt once it starts boiling. Add the Chinese broccoli stems into the pot first, cook for a minute. Add the leafy greens, cook until they turn into a bright green color.
Drain the broccoli and transfer them to a platter. Drizzle the garlic-infused oil, sauce, and sprinkle with toasted garlic and red chili pepper flakes. Serve warm.