Remove tough outer leaves of cabbage halves and core halves. Using a food processor, a mandoline or a knife, shred cabbage as finely as possible.

Peel watermelon radish and cut into matchsticks, then cut matchsticks in half. Alternatively, trim radishes and roughly chop. Stem chilies and deseed them, then chop in pieces smaller than a dime. In a large bowl, mix all ingredients together. Set aside.

In a small bowl, whisk together all ingredients except oil. Let cilantro steep in mixture for a few minutes, then whisk in the oil in a steady stream to emulsify.

Taste and add more lime juice, salt or pepper if needed. Pour over slaw and blend well. Serve.