In a small bowl, whisk the broth with the miso, wine, sugar and cornstarch.
Heat a large wok or skillet until very hot.
Add the oil and chiles and cook over high heat until the chiles darken, 1 to 2 minutes.
Add the garlic and cook for 10 seconds, stirring constantly.
Add the bok choy, season with salt and stir-fry until the leaves are wilted and the stalks are crisp-tender, about 5 minutes.
Stir the miso sauce, add it to the wok and stir-fry until it has thickened slightly, about 2 minutes longer.