Preheat your oven to 350°F (175°C). Grease a 9x13-inch pan.

In a large bowl, whisk together flour, baking soda, salt, and cinnamon.

In a separate bowl, beat butter and sugar until creamy. Add eggs one at a time and finish with vanilla.

Fold dry ingredients into the butter mixture, then gently mix in grated apples and walnuts.

Pour batter into the prepared pan and spread evenly.

Bake for 30-35 minutes; a toothpick should come out clean.

Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.

Beat softened cream cheese and remaining butter until smooth. Gradually add powdered sugar and milk to desired consistency.

Frost the cake once it is completely cool, covering the entire surface.

Slice into squares and serve at room temperature or slightly warmed.