Preheat the oven to 350°F and line a 9x13-inch baking dish with parchment paper.
Whisk the flour, brown sugar, cinnamon, and salt in a large bowl.
Melt 3/4 cup of the butter in a saucepan over medium-low heat until bubbly, then pour it into the dry mixture and stir until crumbly. (This creates a deeper brown butter flavor.) Chill in the refrigerator while you make the batter.
In a large bowl, whisk the cake mix, 4 tablespoons melted butter, oil, vanilla, eggs, and sour cream until smooth.
Spread the batter in the prepared pan. Spoon the apple pie filling over the center, leaving a little batter showing around the edges.
Sprinkle the chilled crumble over the top. You should have a variety of crumble sizes.
Bake for 55 to 60 minutes, until a toothpick inserted in the center comes out clean. Cool completely.
Optional finish: Whisk the powdered sugar and milk together and drizzle over the cake.
Keyword apple breakfast cake, apple coffee cake, apple coffee cake with apple pie filling, apple coffee cake with cake mix, apple crumb cake, cinnamon crumb apple coffee cake, easy apple coffee cake, fall coffee cake, glazed apple coffee cake