Preheat your oven to 350°F (175°C). Grease a 9x5-inch loaf pan and set aside.
In a medium bowl, whisk together the flour, baking soda, salt, cinnamon, and nutmeg. Set aside.
In a large bowl, cream together the butter, granulated sugar, and brown sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the milk and vanilla extract.
Gradually mix in the dry ingredients until just combined. Be careful not to overmix.
Fold in the chopped apples and walnuts (if using).
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for 10 minutes, then remove it from the pan and cool completely on a wire rack.