Preheat and Prepare Pan

Preheat the oven to 350°F (175°C). Lightly grease a 9-inch round cake pan to ensure the cake does not stick.

Mix Wet Ingredients

In a medium bowl, whisk together the eggs and vegetable oil until well blended.

Add Sugars and Flavorings

Incorporate the ground cinnamon, dark brown sugar, granulated white sugar, and vanilla extract into the egg and oil mixture. Mix until thoroughly combined.

Combine Dry Ingredients

In a separate bowl, sift together the all-purpose flour, salt, baking soda, and baking powder. Gradually add the dry mixture to the wet ingredients, stirring gently until just combined. Be cautious not to overmix.

Fold in Apples and Walnuts

Gently fold in the chopped apple and walnuts, ensuring they are evenly distributed throughout the batter.

Transfer to Pan

Pour the batter into the prepared cake pan, spreading it evenly with a spatula.

Bake

Place the cake pan in the preheated oven and bake for approximately 45 minutes, or until a toothpick inserted into the center of the cake comes out clean.

Cool

Remove the cake from the oven and allow it to cool in the pan for about 15 minutes. Afterward, transfer the cake to a wire rack to cool completely before slicing and serving.