Prepare the pan: Preheat your oven to 350°F. Grease a 12-cup (or larger) bundt or flute pan generously with butter or non-stick spray. Bundt pans are notorious for sticking, so don’t be shy with the grease!
Make the apple layer: Pour 5 tablespoons of melted butter evenly into the bottom of the bundt pan. Sprinkle 2/3 cup brown sugar over the butter. Arrange the slices from 2 peeled and cored Granny Smith apples on top. Sprinkle with 1/2 teaspoon cinnamon.
Mix the cake batter: In a large mixing bowl, combine 1 box of spice cake mix, 1 cup water, 3 eggs, 1/2 cup vegetable oil, and 1 (15-ounce) can pumpkin puree. Beat on low speed for 30 seconds, then increase to high speed and mix for about 2 minutes until smooth and well combined.
Assemble and bake: Carefully pour the pumpkin cake batter over the apple layer in the pan. Bake for 45–55 minutes, or until a toothpick inserted in the center comes out clean (baking time can vary depending on the type of pan).
Cool and flip: Run a thin knife around the edges of the cake to loosen it. Allow the cake to cool in the pan on a wire rack for 10–15 minutes, then carefully invert it onto a serving plate.
Make the cream cheese glaze: In a medium bowl, beat 4 ounces of softened cream cheese until light and fluffy. Add 1/2 cup confectioners’ sugar and 1/2 teaspoon vanilla extract, mixing until smooth. Add milk, 1 tablespoon at a time, until the glaze reaches a pourable consistency (slightly runny, but it will firm up as it sits on the cake).
Glaze and serve: Transfer the glaze to a piping bag or plastic bag, snip the corner, and drizzle it over the cooled cake. Slice and enjoy!