Preheat oven to 350 F. Grease a 9 x 9 inch baking dish.
In a large bowl, beat together the melted butter, sugar, and egg until fluffy. Fold in the apples and walnuts. In a separate bowl, sift together the flour, salt, baking powder, baking soda, and cinnamon. Stir the flour mixture into the wet mixture until just blended. Spread the batter evenly in the prepared baking dish.
Bake 35 minutes in the preheated oven, or until a toothpick inserted in the center comes out clean.