How to Make It
Preheat the oven to 350°. In a small bowl, cover the porcini with the hot water and let soak until softened, about 15 minutes. Using a slotted spoon, remove the porcini from the soaking liquid; discard the liquid. Rinse and coarsely chop the porcini.
In a large saucepan, combine the wine, garlic and thyme sprigs and boil over high heat until the wine has reduced by half, about 3 minutes. Add the cream, 1 cup of the grated cheese, the salt and cayenne and bring to boil. Remove from the heat and discard the thyme sprigs and garlic cloves.
Arrange half of the potato slices in an even layer in a shallow, 15-by-10-inch baking dish. Spread the porcini evenly over the potatoes. Top with the remaining potato slices. Pour the cream mixture on top and shake the dish to distribute the cream. Sprinkle with the remaining 1/2 cup of grated cheese. Bake for 1 hour and 10 minutes, or until the potatoes are tender and the top is richly browned. Let the gratin rest for 15 minutes, then serve hot.