Preheat the oven to 350°F. Grease an 8½x4½-inch loaf pan and line with parchment paper, allowing excess to hang over the long sides of the pan.

Prepare the apple by either grating it using the largest holes on a cheese grater or chopping it into small pieces (about ½-inch cubes). Set aside.

In a medium bowl, whisk together flour, granulated sugar, brown sugar, cinnamon, baking soda, baking powder, salt, and nutmeg. Add the beaten eggs and melted butter to the flour mixture, and stir together until just a few dry streaks of flour remain.

Add the grated or chopped apple and nuts (if using) to the batter and stir until evenly combined. Pour into the prepared pan and smooth out the top. Sprinkle with additional granulated sugar, if desired.

Bake for 55 to 65 minutes or until a wooden pick inserted in the center comes out clean.

Let the bread cool in the pan on a wire rack for 10 minutes. Remove the loaf from the pan and let cool for about 30 minutes more. Slice and serve warm.