Discard the core of green and red cabbages and thinly slice them or shred them using a cabbage slicer.
Peel the carrots. Then, using a julienne peeler, make long, thin julienned strips with the carrot. When they are too long, cut the long strips in half or thirds into 2-inch pieces. If you have a regular vegetable peeler, peel the carrot into thin sheets, then cut the sheets into long, thin julienned strips.
Chop cilantro and discard the stems.
In a large salad bowl, place the green cabbage, red cabbage, carrot, cilantro, shelled edamame, and peanuts. If you're not serving the salad right away, cover it with plastic and refrigerate it for up to 24 hours.