Place potatoes in salted boiling water for 10 minutes, or until barely tender. Drain and immerse in ice water to stop cooking process. Combine with corned beef, 11/4 cups onion, salt, pepper and nutmeg. Mix well and if time permits, refrigerate up to overnight to allow flavors to blend.
Heat 2 Tbsp oil in a large, heavy skillet over medium-high heat. Add hash and press down with spatula. Reduce heat to medium and cook until golden brown on bottom (try not to disturb). Turn hash over and brown other side.
Meanwhile, heat butter and remaining 1 Tbsp oil in a large skillet over medium-high heat. Add remaining 1/2 cup onion and sauté for 2 minutes. Add cabbage and carrot and cook until tender-crisp. Season to taste with salt and pepper.
To serve, place sautéed cabbage on a platter and top with hash.
Servings: 6