Melt 1/2 cup butter in a Dutch oven over medium heat. Arrange layers of rutabaga, turnips, and carrots over butter. Place two sheets of waxed paper on top of vegetables; cover with lid. Cook over high heat until steam begins to escape. Reduce heat to low, and cook 20 minutes without removing lid.
Add broccoli; cover and cook 20 minutes over medium heat or until broccoli is tender. Place vegetables in a serving dish. Add salt and pepper to taste. Pour butter over vegetables.