Preheat your oven to 350°F (175°C) and grease a 9-inch round baking pan.

In a large mixing bowl, cream the softened butter, granulated sugar, and dark brown sugar until light and fluffy.

Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract.

In a separate bowl, whisk together the all-purpose flour, baking soda, ground cinnamon, and salt. Gradually add to the wet ingredients.

Fold in the chopped apples and walnuts gently.

Pour the batter into the prepared pan and bake for 40-45 minutes until a toothpick comes out clean.

Let the cake cool in the pan for 10-15 minutes, then transfer to a wire rack to cool completely.