Preheat your oven to 350°F (175°C) and prepare a 9-inch round cake pan with non-stick spray or softened butter.

In a large mixing bowl, cream together 1/4 cup of softened butter, 1/4 cup of granulated sugar, and 1/4 cup of dark brown sugar until light and fluffy, about 2-3 minutes.

Incorporate 2 large eggs one at a time into the creamed mixture, then stir in 1/4 teaspoon of vanilla extract.

In a separate bowl, whisk together 1 1/4 cups of all-purpose flour, 1 teaspoon of baking soda, 1 teaspoon of ground cinnamon, and 1/4 teaspoon of salt.

Gradually blend the dry ingredients into the wet ingredients until just combined.

Gently fold in 2 cups of chopped peeled apples and 1/2 cup of chopped walnuts, being careful not to break up the apple pieces too much.

Transfer the batter into the prepared cake pan and smooth the top. Bake for 40-45 minutes, or until a toothpick comes out clean or with a few moist crumbs.

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