Trim the beans and cut into 1-inch pieces. Peel the carrots and cut into 2-inch lengths, then cut each piece lengthwise into quarters and halve these.
Finely chop the green chilies. Peel the ginger and cut into paper-thin slices. Stack a few slices together at a time and cut them into minute dice. If using fresh galangal, peel and dice it in the same way. Peel and finely chop the garlic and shallots.
Set a wok over a high heat and swirl in the oil. When the oil is hot, put in the chilies, ginger, galangal, garlic, shallots, and curry (or bay) leaves. Stir and fry briefly until the spices start to brown.
Add the green beans, carrots, and salt. Stir and fry for 1 minute. Pour in 3/4 cup water and cover with a lid. Turn the heat to medium and cook for about 5 minutes or until the vegetables are just tender.