Place a little oil in a wok/frying pan over medium to high heat. Add the carrots, galangal (or ginger), and shiitake mushrooms. When the wok/pan becomes dry, add a little of the wine or sherry, 1 Tbsp. at a time, to keep ingredients frying nicely. Stir-fry in this way, adding more wine or sherry as needed, for 3-4 minutes, or until carrots start to soften.
Add the rest of the vegetables and continue stir-frying another 2-5 minutes, or until the broccoli has softened but still retains some of its crispness.