Preheat oven to 350 degrees F (175 degrees C). Grease and flour an 8x8-inch baking pan.
In a large bowl, mix melted butter with sugar and egg. Mix in flour, baking soda, and cinnamon, and then stir in apple and walnuts. Spread batter into prepared pan.
Bake for approximately 40 minutes, or until a small knife inserted in the center comes out clean.
