Mince and mash the chopped garlic to a paste with a pinch of salt. Stir together the scallions, minced garlic, soy sauce, sesame oil, water, hot red-pepper flakes and sugar together in a small bowl. Set aside.
Heat the oil in a wok or large skillet over high heat. Add the cabbage, season with a pinch of salt, and stir-fry, using tongs to stir, until the cabbage is just wilted, 3 to 5 minutes.
Remove from the heat and pour the dressing over the cabbage and toss gently to combine.
Transfer to a serving dish and garnish with the toasted sesame seeds.
The sauce can be made 2 hours ahead and kept at room temperature.