1. Preheat oven to 350°F (175°C). Grease a 9×13-inch baking pan and, if desired, line it with parchment paper for easy removal.

2. In a large bowl, combine yellow cake mix, sour cream, 3 eggs, vegetable oil, and 2 teaspoons vanilla extract. Beat until the batter is thick and smooth with no dry streaks.

3. Spread a little more than half of the cake batter evenly into the prepared pan, smoothing it into the corners.

4. In a separate bowl, beat softened cream cheese until completely smooth. Add granulated sugar, the remaining 1 egg, and 1 teaspoon vanilla extract, mixing until creamy and lump-free.

5. Pour or spoon the cream cheese mixture evenly over the batter in the pan, leaving a small border around the edges if possible.

6. Dollop the remaining cake batter over the cream cheese layer and gently spread it as evenly as you can. It’s fine if some cream cheese peeks through.

7. In another bowl, whisk together all-purpose flour, brown sugar, cinnamon, and salt. Stir in the melted butter until large, clumpy crumbs form.

8. Scatter the crumb topping evenly over the entire surface of the cake, covering as much of the batter as possible.

9. Bake for 30–35 minutes, or until the top is golden and a toothpick inserted into the cake (avoiding the cream cheese pockets) comes out with just a few moist crumbs.

10. Let the coffee cake cool in the pan on a wire rack for at least 30 minutes so the layers can set.

11. In a small bowl, whisk together powdered sugar and 2 tablespoons milk or cream until smooth and pourable, adding the remaining milk if needed to thin.

12. Drizzle the glaze over the cooled or slightly warm coffee cake, then slice into squares and serve warm or at room temperature.