Remove the outer layers of the cabbage and cut the cabbage heads in half.

Slice cabbage into thin pieces that resemble noodles. Keep the colors separate so that they do not leak.

Thinly slice the shallots.

In the frying pan, heat the avocado oil.  Add shallots, cover, and cook on a low flame until golden.  Remove shallots and set aside.

Add the cabbage in small batches, one color at a time.  Cook each batch covered on a medium-low flame for 10 minutes, then uncover and cook for an additional 10-15 minutes.

When all the cabbage is cooked, combine shallots and both colors of cabbage. Season with salt and pepper. Toss and serve.