Preheat the oven to 350°F. Line a 9 x 13-inch baking dish with parchment paper, leaving enough overhang to make the cake easier to lift out after cooling.
Add ¾ cup butter to a small saucepan and melt over medium-low heat. Continue cooking, stirring occasionally, until the butter begins to bubble.
In a large bowl, whisk together the flour, brown sugar, cinnamon, and salt, breaking up any lumps in the brown sugar.
Pour the melted butter into the flour mixture and gently stir until all the dry ingredients are moistened. The mixture should be crumbly rather than smooth. Place the crumble topping in the refrigerator while you make the cake batter.
In a separate large bowl, whisk together the cake mix, 4 tablespoons melted butter, vegetable oil, vanilla, eggs, and sour cream until well combined and smooth.
Transfer the batter to the prepared baking dish and spread it into an even layer.
Spoon the apple pie filling over the center of the batter, spreading it out while leaving a small border of cake batter visible around the edges.
Remove the crumble mixture from the refrigerator and sprinkle it evenly over the apples. Use your fingers to gently break apart any pieces that are especially large.
Bake for 55-60 minutes, or until the cake is baked through and a toothpick inserted near the center comes out without wet cake batter.
Let the coffee cake cool. Whisk together the powdered sugar and milk until smooth, then drizzle the glaze over the top before slicing and serving.
Enjoy!