Put the potatoes and cauliflower in a medium pot and cover with cold water by at least an inch.
Bring the pot to a boil over high heat, reduce the heat to medium-low, and cook until the vegetables are tender, about 12 minutes.
While the potatoes are cooking, heat a large skillet over medium heat and add the cabbage and green onion.
Cook the cabbage mixture for 7 to 8 minutes until it is tender. Add water 1 to 2 tablespoons at a time, as needed, to keep them from sticking to the pan.
Drain the potato cauliflower mixture in a colander, reserving some of the cooking liquid. Return the vegetables to the pan.
Mash the potato cauliflower mixture to the consistency you prefer.
Add the cabbage to the pan with the potatoes. Season with salt and pepper and mix well.