Preheat the oven to 350 degrees F (175 degrees C). Grease and flour an 8-inch square baking pan.

Stir sugar, melted butter, and egg together in a large bowl. Mix in flour, cinnamon, and baking soda, then stir in apple and walnuts. Spread batter into the prepared pan.

Bake in the preheated oven until a small knife inserted in the center comes out clean, about 40 minutes. Cool completely before cutting into nine bars.