Preheat oven to 350°F. Grease a 9x9 inch baking dish with butter.
In a skillet over medium heat, melt 2 oz of butter. Add sliced cabbage and sauté for 5 minutes until slightly softened.
In a large bowl, combine mashed potatoes, mashed turnips, sautéed cabbage, remaining 1 oz butter, salt and pepper. Mash together well.
Transfer mixture to prepared baking dish and spread evenly. Top with grated cheddar cheese.
Bake for 30 minutes covered with foil. Uncover and bake 5 more minutes until top is lightly browned.
Let sit 5 minutes before serving. Enjoy!