Drain the potatoes, and transfer them to a large mixing bowl. Use a potato masher or an electric mixer to mash the potatoes. Add brie, heavy cream, butter, salt, thyme, and pepper. Stir to combine.
6 ounces brie cheese, ½ cup heavy cream, 4 tablespoons unsalted butter, 1 teaspoon salt, 1 teaspoon fresh thyme leaves, ¼ teaspoon white pepper