Preheat the oven to 400°F. Grease a 9x13-inch baking dish; set aside.
In a medium bowl, whisk together the heavy cream, milk, flour, garlic, salt and pepper. Set aside.
Slice potatoes into 1/8 inch thick rounds. (I use my mandolin slicer.)
Spread 1/3 of the sliced potatoes in the prepared dish. Pour 1/3 of the garlic cream mixture evenly over the potatoes. Repeat this process two more times, ending with the cream mixture. Sprinkle the fresh Parmesan cheese evenly over the top. Cover dish with foil and bake for 30 minutes.
Carefully remove foil (it will be hot!) and bake another 20 minutes, or until potatoes are tender and golden-brown. Remove from oven and let stand 5 minutes. Top with freshly chopped parsley or chives, if desired. Serve and enjoy!