Cut into the top of one cabbage and carefully hollow it out, leaving 3–4 outside leaves intact. Reserve the hollowed-out inner portion. Plunge the hollowed-out head into a large amount of boiling water and simmer for 5 minutes, or until it's tender-crisp but still holds its shape. Quickly cool it in cold water, then invert and drain.
Chop the reserved cabbage pieces and measure out 1 1/2 cups. In a pan, stir-fry these chopped cabbage pieces in butter along with the green onions until they are tender. Set this mixture aside.
Boil and mash the potatoes, incorporating milk, salt, and pepper until smooth. Finally, stir in the sautéed cabbage and green onion mixture, along with the fresh parsley, until everything is well combined.