Melt the butter: Add the butter, brown sugar, and heavy cream to an 8 x 8-inch baking dish. Set the baking dish in the oven and preheat the oven to 350°F.
Meanwhile, prepare the batter: In a bowl, combine the milk, flour, granulated sugar, baking powder, salt, and vanilla extract, and whisk to incorporate evenly.
Assemble: Once the butter is melted in the oven, about 4-6 minutes, remove the baking dish. Whisk to combine the ingredients in the pan. Then, add the sliced apples, cinnamon, and allspice, and toss to coat the apples. Pour the batter over the top. There is no need to stir.
Bake in the preheated oven until the cobbler is golden and set in the middle, 45-55 minutes. Once baked, remove from the oven and cool for 15 minutes before serving.
