Peel the potatoes and slice them into 1/8-inch thick rounds—I recommend using a mandoline slicer for uniform thickness, which ensures even cooking throughout the dish. Preheat your oven to 400°F and lightly grease a 9x13-inch baking dish (or similar 3-quart capacity dish) with butter or oil.
In a medium pot over medium heat, combine the heavy cream, half-and-half, and crumbled Boursin cheese. Stir frequently until the cheese melts completely and the mixture is smooth and creamy, about 3-4 minutes. Add the garlic powder and ground nutmeg, then season with salt and pepper to taste. I like to taste as I go here—the Boursin is already quite flavorful and herbed, so you may need less salt than you'd expect.
Spread half of the sliced potatoes evenly across the bottom of your prepared baking dish, then season lightly with salt and pepper. Pour half of the Boursin cream sauce from Step 2 over this layer. Arrange the remaining potatoes on top in an even layer and season again with salt and pepper. Pour the remaining cream sauce over the final potato layer, making sure to distribute it evenly so all potatoes are partially submerged.
Place the dish in the preheated 400°F oven and bake for 55-60 minutes, until the potatoes are fork-tender and the top is golden brown. You can test doneness by inserting a knife through the center—it should slide through with minimal resistance. Let the dish rest for 5 minutes out of the oven before serving, which allows the cream to set slightly and makes plating easier.
Remove the baking dish from the oven and sprinkle the finely snipped chives evenly across the top. The residual heat will slightly soften them while maintaining their fresh flavor and vibrant color.