1. Preheat your oven to 350°F (175°C) and grease a springform pan.
2. In a large mixing bowl, mix cake mix, melted butter, and one egg until a dough forms.
3. Press the dough evenly into the greased pan, ensuring it slightly raises along the edges to hold the filling.
4. In a medium saucepan, melt 2 tablespoons of butter over medium heat.
5. Add diced apples, brown sugar, and cinnamon to the saucepan, cooking for about 15 minutes until soft and fragrant.
6. Let the cooked apples cool slightly, then spread them evenly over the prepared crust.
7. In a separate bowl, beat cream cheese until smooth and creamy.
8. Gradually add the remaining eggs, vanilla extract, and powdered sugar to the cream cheese, mixing thoroughly after each addition.
9. Pour the cream cheese mixture evenly over the apple layer, smoothing it with a spatula.
10. Place the pan in the oven and bake for 35-50 minutes, or until the edges are golden brown and the center is slightly jiggly.
11. Remove the cake from the oven and allow it to cool completely in the pan.
12. Chill the cake in the refrigerator for a couple of hours to set the cream cheese layer before serving.
13. Slice and enjoy your Apple Gooey Butter Cake, storing leftovers in an airtight container in the refrigerator for up to three days.