Preheat your oven to 350°F (175°C). Lightly grease a 9x9-inch square baking pan or a 9-inch round cake pan. For easy removal, consider lining the bottom with parchment paper, leaving small overhangs on opposite sides to create "handles" for lifting.
Peel, core, and dice your apples into roughly 1/2-inch cubes. Toss them with 1 tablespoon of lemon juice to prevent browning if you're working ahead. Pat them dry with a paper towel before incorporating them into your batter to prevent excess moisture.
In a large bowl, whisk together the flour, sugar, baking powder, salt, cinnamon, and nutmeg until well combined and no lumps remain.
In a separate medium bowl, beat the eggs lightly, then add the oil, milk, and vanilla extract. Whisk until smooth and fully incorporated.
Make a well in the center of your dry ingredients and pour in the wet mixture. Stir gently with a rubber spatula just until combined - about 15-20 strokes. Avoid overmixing.
Gently fold in your diced apples, ensuring they're evenly distributed throughout the batter. This step should take no more than 10-12 folds to maintain the light texture of your cake.
In a small bowl, mix brown sugar and cinnamon. Add melted butter and stir until the mixture resembles wet sand. If using nuts, fold them in now for that perfect textural contrast.
Pour the batter into your prepared pan, smoothing the top with your spatula. Sprinkle the cinnamon-sugar mixture evenly over the top, gently pressing it into the batter slightly.
Bake in your preheated oven for 40-45 minutes, or until a toothpick inserted into the center comes out clean with a few moist crumbs. The cake should pull away slightly from the edges of the pan when done.
Allow your cake to cool in the pan for 15 minutes before transferring to a wire rack to finish cooling. This patience rewards you with perfect slices that hold their shape.