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

Cream together the softened butter, granulated sugar, and dark brown sugar until light and fluffy.

Add eggs one at a time, incorporating each before the next, then mix in vanilla extract until smooth.

In another bowl, whisk together flour, baking soda, ground cinnamon, and salt. Gradually add dry ingredients to the wet mixture.

Fold in chopped apples and walnuts carefully.

Pour the batter into the prepared pan and spread evenly.

Bake for 40-45 minutes, or until a toothpick comes out clean.

Cool the cake in the pan for 10-15 minutes before transferring to a wire rack to cool completely.

Slice and serve warm, topped with powdered sugar or vanilla ice cream if desired.