Preheat the oven to 350°F (175°C) and prepare a 9x13-inch baking pan by greasing it with butter and dusting with flour.

In a large mixing bowl, combine the all-purpose flour, granulated sugar, brown sugar, baking powder, salt, ground cinnamon, and ground nutmeg.

In another bowl, whisk together the melted unsalted butter, vegetable oil, eggs, and vanilla extract until smooth.

Add the wet ingredients to the dry ingredients and gently stir until just combined.

Fold in the chopped apples and optional nuts until evenly distributed.

Spoon the batter into the prepared baking pan and spread evenly.

Bake for 45 to 50 minutes, or until a toothpick comes out clean.

Cool in the pan on a wire rack for about 10 minutes.

Dust with powdered sugar if desired, slice into squares, and serve.