1. Preheat oven to 350°F (175°C). Grease a 9-inch square baking pan and line the bottom with parchment paper.

2. Peel, core, and thinly slice the apples, then toss them with the lemon juice and set aside.

3. In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg until well combined.

4. In a large mixing bowl, whisk the granulated sugar, brown sugar, melted butter, and oil until smooth and glossy.

5. Add the eggs one at a time, whisking well after each addition, then whisk in the vanilla extract.

6. Whisk in the buttermilk until the mixture is smooth and fully combined.

7. Add the dry ingredient mixture to the wet ingredients in two additions, folding gently with a spatula just until no streaks of flour remain.

8. Spread about two-thirds of the batter into the prepared pan in an even layer.

9. Arrange half of the sliced apples over the batter.

10. Dollop the remaining batter over the apples and gently spread it out, then arrange the remaining apple slices over the top, lightly pressing them into the batter.

11. In a small bowl, stir together the topping sugar and cinnamon. Drizzle the melted butter evenly over the top of the cake, then sprinkle the cinnamon sugar all over.

12. Bake for 40–45 minutes, or until the top is deeply golden and a toothpick inserted into the center comes out with just a few moist crumbs.

13. Let the cake cool in the pan on a wire rack for at least 20–30 minutes before slicing.

14. Serve warm or at room temperature, plain or with whipped cream or ice cream if desired.