Scrub the potatoes, but don't peel them. Cut them into quarters or eighths if they are very large. Put the potatoes into a 4-quart saucepan with enough water to cover by 1-inch. Cover the saucepan and bring it to a boil over high heat. Lower the heat to medium-high and boil gently for about 8 to 10 minutes, or until the potatoes are fork tender.
Meanwhile, put 3 cups of the purple cabbage, all the green cabbage, and the water into a large, deep skillet. Cover, and steam over high heat for about 5 to 7 minutes, or until the cabbage is tender.
Remove the cover, add the olive oil, and cook and stir for 1 to 2 minutes or until the cabbage is thoroughly softened. Set aside.
Transfer the cooked potatoes to a large bowl and mash them with enough soymilk to create a smooth, creamy consistency. Season with the nutritional yeast flakes, if using, along with salt and pepper. Add the mashed, seasoned potatoes to the cabbage along with half the green onions and mix together.
Transfer the Colcannon to an attractive serving bowl or platter and garnish the top with the remaining green onions. Finish by garnishing the perimeter of the bowl or platter with the remaining purple cabbage.