Pre-heat oven to 400 degrees and use the softened butter to generously grease a baking dish that measures 9 x 13 x 2 inches (or equivalent)
Add the cream, half and half cream, garlic, and ¼ tsp salt to a medium sauce pan. Bring the liquid to a boil over medium heat, then decrease the heat to medium-low and allow to simmer for another 20 minutes. Remove the pan from the heat, and set aside.
Reserve the most uniform and attractive sweet potatoes slices for the top layer. Use any broken or small slices of sweet potato in the middle layers.
To assemble the Gratin, spoon approximately ¼ cup of the cream into the bottom of the prepared baking dish. Place a layer of sweet potatoes, slightly over lapping in the bottom of the dish. Ladle another ¼ cup of the cream over the sweet potatoes, sprinkle about 1/4-1/2 tsp each of the fresh sage and dried thyme, as well as a pinch of salt & pepper, and finally 1 Tbsp. of parmesan cheese. Continue the layers until you run out of potatoes. When you get to the last layer pour all the remaining cream over the top, add herbs, salt and pepper, but do not sprinkle the final layer of cheese.
Lay a sheet of aluminum foil loosely over the top, and bake covered for about 30-35 minutes, then remove the foil and bake for another 20 minutes.
Sprinkle the remaining cheese over the top of the potatoes and bake for additional 15 minutes or until potatoes are cooked.
The gratin is done when a paring knife is easily inserted into the center. Remove from the oven and allow to cool for about 10 minutes before serving.