Preheat your oven to 350°F (175°C) and grease a 9x9 inch baking dish with butter.

Melt 2 oz of unsalted butter in a skillet and sauté the thinly sliced cabbage for about 5 minutes.

In a mixing bowl, combine the mashed potatoes, mashed turnips, and sautéed cabbage. Add remaining butter, salt, and pepper, mixing well.

Transfer the mixture into the greased baking dish, spreading it evenly.

Sprinkle grated sharp cheddar cheese evenly across the top of the casserole.

Cover with aluminum foil and bake for 30 minutes, then remove foil and bake for an additional 5 minutes until cheese is golden and bubbling.

Let the casserole cool for 5 minutes before serving.