Special Equipment: mandolin, 11 by 7-inch baking dish
Preheat the oven to 375 degrees F.
Put the cream, garlic, thyme and cayenne in a saucepan and season it with salt. Taste to make sure it is adequately seasoned. Bring the cream to a boil and then turn off the heat. Let the mixture steep for 15 to 20 minutes.
Butter the baking dish and layer in 1/3 of the sliced turnips. Sprinkle 1/3 of the grated cheese over the turnips and dot with 1/3 of the butter. Remove the thyme and garlic from the cream and pour 1/3 of the cream over the turnips. Repeat this process 2 more times until all of the ingredients are used up.
Cover the dish with foil, place on a baking sheet and bake in the preheated oven for 35 to 40 minutes. Remove the foil and bake for another 20 minutes, until golden. When done a fork should slide in and out of the center of the dish easily.
For easier serving, let the dish rest 10 to 12 minutes before serving.