Preheat oven to 350°F and grease a 9x5 inch loaf pan.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, and cinnamon.
In a separate bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla.
Stir the wet ingredients into the dry ingredients until just combined. Fold in the apples, walnuts, and brown sugar.
Pour the batter into the prepared loaf pan and bake for 45 minutes, or until a toothpick inserted into the center comes out clean.
Allow to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.