Preheat the oven to 350˚F. Grease a 9×13-inch baking pan and/or line it with parchment paper; set aside. Peel and seed the apples, then chop them into small pieces.

In an electric mixer with a paddle attachment, beat the butter and sugar on medium speed until creamy. Add the eggs and vanilla extract, and continue to beat until fluffy, approximately 2 minutes.

Stir in the chopped apples and walnuts by hand.

In a separate bowl, whisk together the flour, baking soda, baking powder, cinnamon, and salt. Mix the dry ingredients into the wet mixture until well combined.

Pour the batter into the greased and lined pan, and level it with a fork. Bake for 40-45 minutes until the top is golden brown. Cool the brownies on a wired rack completely. Cut into bars to your desired size.