Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, ground cinnamon, and salt. Set aside.
In a large bowl, beat the eggs and sugar together until light and fluffy.
Add the vegetable oil, plain Greek yogurt, and vanilla extract to the egg mixture and mix until well combined.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix.
Fold in the diced apples and chopped walnuts (if using) until evenly distributed.
Pour the batter into the prepared cake pan and spread it evenly.
Bake for 40 to 45 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Transfer the cake to a wire rack to cool completely before serving.