Remove core from napa cabbage; discard core. Cut the cabbage crosswise into thin shreds to make about 2 quarts. Cut the radicchio in half through core; remove and discard core. Cut the radicchio into thin shreds to make about 1 quart.
Place a wok or 5- to 6-quart pan over high heat. When the pan is hot, add salad oil, the garlic and ginger, and the fennel seed; stir 30 seconds. Add the napa cabbage, the radicchio, and the soy sauce; cover pan and cook for 1 minute. Remove pan lid, and stir-fry until vegetables wilt, about 2 minutes longer. Stir in half of the chopped cilantro and all of the sesame oil.
Transfer vegetables to a serving dish; sprinkle with remaining cilantro and sesame seed before serving.