Preheat oven to 350 degrees F. Grease a 9 by 9 baking dish or 1.5 quart dish.
Peel the turnips and slice thinly about an ⅛th of an inch or use a mandolin.
Whisk together the cream, garlic, melted butter, salt and pepper and 1 tablespoon thyme.
Layer one third of the turnip slices on the bottom of the dish. Pour one third of the cream mixture over the turnips. Sprinkle a half cup of mozzarella over that. Repeat this process for the second and third layers. You will have 1 cup of mozzarella remaining.
Cover and bake for 1 hour and 15 minutes or until turnips are soft. Remove cover, sprinkle remaining cheese over the top and bake 10-15 minutes until cheese is melted and bubbling. Serve with remaining tablespoon of thyme.