Preheat the oven to 375 degrees. In a large oven proof skillet, over medium high heat, warm the olive oil and then place a layer of turnip slices (slightly overlapping them) on the bottom of the skillet. Sprinkle with about 1/3 of the ham and garlic and drizzle with a bit of the chicken broth, cream, salt and pepper and then sprinkle with some of the cheese.
Repeat these steps a couple more times, leaving the pan on the hot stove throughout the process. By the time, you finish the layers, the pan should be bubbling. When the layers are done, top with any remaining cheese. Bake for about 20 minutes, or until the cheese on top starts to turn golden brown. Enjoy!