Preheat your oven to 350°F (175°C) and grease the baking dish with about 1 oz of unsalted butter.

Melt 2 oz of butter in a skillet over medium heat and sauté the cabbage for approximately 5 minutes until soft.

In a large mixing bowl, mix the boiled and mashed potatoes with turnips, sautéed cabbage, remaining butter, salt, and pepper. Mash until smooth.

Spread the mixture into the prepared baking dish, pressing down slightly to eliminate air pockets.

Sprinkle the grated cheddar cheese on top, cover with aluminum foil, and bake for 30 minutes.

Remove the foil and bake for an additional 5 minutes until the top is lightly browned and bubbly. Let sit for 5 minutes before serving.