Combine diced apples, 1/4 cup brown sugar, 1 teaspoon cinnamon, nutmeg, and lemon juice in a saucepan; cook over medium heat for 5-7 minutes until apples soften slightly. Whisk together cornstarch and 1 tablespoon water or apple cider until smooth, then add this mixture to the apples and stir until the filling thickens. Remove from heat and let cool completely.

Preheat your oven to 350°F (175°C) and grease and flour a 9x13 inch baking dish. In a large bowl, beat softened butter and 1 cup granulated sugar until light and fluffy, then beat in the eggs one at a time, followed by vanilla extract. In a separate bowl, whisk together flour, baking powder, and salt; gradually add these dry ingredients to the wet ingredients, alternating with milk, mixing until just combined without overmixing.

In a small bowl, combine melted butter, 1/2 cup brown sugar, and 1 tablespoon ground cinnamon, stirring until a thick paste forms.

Spread half of the cake batter evenly into the prepared baking dish, then spoon half of the cooled apple pie filling over the batter. Drizzle half of the cinnamon swirl mixture over the apples, and repeat these layers with the remaining cake batter, apple filling, and cinnamon swirl. Using a knife or skewer, gently swirl through the layers to create a marbled pattern.

Bake for 35-45 minutes, or until a toothpick inserted into the center comes out clean or with moist crumbs. Let the cake cool in the pan on a wire rack.

While the cake cools, beat softened cream cheese and 2 tablespoons butter in a medium bowl until smooth. Gradually add powdered sugar and vanilla extract, beating until creamy, then add milk or cream, one teaspoon at a time, until the glaze reaches your desired drizzling consistency. Once the cake has cooled slightly (it can still be warm), drizzle the cream cheese glaze generously over the top.

Slice and serve warm. Enjoy!