Preheat your oven to 350°F (175°C). Grease a 9x9 inch baking dish with 1 oz of unsalted butter.

In a large skillet over medium heat, melt 2 oz of unsalted butter. Add thinly sliced green cabbage and sauté for about 5 minutes until tender.

In a large mixing bowl, combine well-mashed russet potatoes and turnips, sautéed cabbage, remaining 1 oz of butter, 1/2 teaspoon of kosher salt, and 1/4 teaspoon of black pepper. Mix until thoroughly incorporated.

Transfer the mashed mixture into the prepared baking dish, spreading it evenly. Sprinkle grated sharp cheddar cheese across the top.

Cover with aluminum foil and bake for 30 minutes. Remove foil and bake uncovered for 5 more minutes until cheese is bubbly.

Let the dish cool for about 5 minutes before serving. Scoop onto plates and enjoy.