Combine soy sauce and cooking wine with cornstarch in a small bowl.
Heat oil in wok over high heat. (I often use a cast iron skillet for stir-frying, but a bunch of watercress is bulky to start with, and though it wilts down on cooking like most greens, without a wok much of it would wind up on the stovetop and floor.)
Add the ginger, garlic, and red pepper. Stir till fragrant (perhaps 30 seconds).
Add the watercress and stir immediately and continuously. It should wilt down in a minute or two. If necessary, add a tablespoon or two of water and cover for half a minute, but the leaves should release water as they wilt.
When the stems are slightly wilted but not limp, re-suspend the cornstarch in the soy sauce mixture and add to the wok. Give it a quick stir and serve immediately over rice, drizzling a few drops of sesame oil over it if desired.
Don't overcook this. The color should still be bright green and the stems al dente. Cooking time should be under 3 minutes.