Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, ground cinnamon, and salt.
In a large bowl, combine the granulated sugar, brown sugar, and egg. Beat until smooth and creamy.
Add the plain yogurt, vegetable oil, and vanilla extract to the sugar and egg mixture. Mix until well combined.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix.
Fold the diced apples into the batter evenly.
Pour the batter into the prepared cake pan and spread it evenly.
Bake in the preheated oven 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.