Remove any tough outer leaves from the cabbage, and remove the core. Shred remaining cabbage leaves. Slice each fennel bulb in half lengthwise, and remove the core. Thinly slice fennel widthwise (against the grain). Place shredded cabbage and sliced fennel in a large bowl, then sprinkle with kosher salt. Let sit at room temperature for 15 minutes.
Squeeze the liquid from the cabbage and fennel, then place in a medium bowl. You can do this with your hands or a kitchen towel (I used my hands - it's kindof fun). Discard the liquid.
Add the green onion, garlic, ginger, chile paste, fennel seeds, sugar and rice vinegar to the bowl with the cabbage and fennel, tossing to combine. You can enjoy immediately, but I let the mixture sit at room temperature for 2 hours to let the flavors mingle a bit more. Store up to 1 month in the refrigerator.