Combine the broth, soy sauce, sugar, rice wine, and 1/3 cup water in a small bowl. Stir to dissolve the sugar and set aside.
Heat the oil in a wok or 12-inch skillet over medium heat until hot. Add the white parts of the scallions, garlic, and ginger and cook, stirring constantly, until fragrant but not brown, 30 seconds. Add the squash, increase the heat to medium high, and cook, stirring occasionally, until the squash begins to soften and the aromatics brown slightly, about 3 minutes.
Reduce the heat to medium, add the soy sauce mixture, and stir, scraping the bottom of the pan with the spoon to loosen any stuck-on aromatics. Cover and simmer until the squash is just tender when pierced with a fork, 4 to 6 minutes. Transfer to a serving dish and garnish with the scallion greens.