Preheat the oven to 350˚. Butter a 9 x 13-inch baking dish. Combine the half-and-half and heavy cream in a large measuring cup. Using a mandoline or a very sharp knife, slice the potatoes very thinly. Place the potatoes in a large bowl. Drizzle with half of the half-and-half/cream mixture and set aside. In a large skillet over medium-low heat, melt the butter. Add the garlic and onion and cook, stirring occasionally, until translucent, about 4 minutes. Cut the bar of cream cheese in half and add both halves to the skillet, stirring constantly. Continue stirring until the mixture is smooth and combined, about 3 minutes. Stir in the remaining half-and-half/cream mixture and season with the salt and pepper. Stir in the thyme, then stir in 1/2 cup of the grated parmesan. Pour the cream-soaked potatoes into the baking dish. Pour the cream cheese mixture over the top, scraping out the skillet to get every last drop. Sprinkle the remaining 1/2 cup grated parmesan over the top. Cover with foil and bake 30 minutes. Remove the foil and continue baking until the potatoes are tender and the top is golden brown and bubbly, at least 45 minutes more. Remove from the oven and let stand for 10 minutes. Sprinkle with the chives, then cut into squares and serve.