Preheat your oven to 350°F (175°C). Grease a 9-inch round cake pan with butter or non-stick cooking spray, and line the bottom with a circle of parchment paper to ensure easy removal.

In a medium mixing bowl, whisk together the all-purpose flour, baking soda, baking powder, ground cinnamon, and salt. Make sure the spices are evenly distributed throughout the dry mixture.

In a separate large bowl, use a hand mixer to beat the softened butter and granulated sugar together until light, fluffy, and pale in color, about 2 to 3 minutes. Add the eggs one at a time, beating well after each addition, then stir in the vanilla extract.

Gradually add the dry flour mixture into the wet ingredients, mixing on low speed until just combined. Be careful not to overmix the batter, as this can result in a tough, dense cake.

Gently fold the diced apples into the batter using a rubber spatula. The batter will be quite thick, but don't worry, the apples will release their natural moisture as the cake bakes.

Spoon the thick batter into the prepared cake pan, spreading it out and smoothing the top to ensure an even layer. Bake in the preheated oven for 40 to 45 minutes, or until a toothpick inserted into the center comes out clean and the top is a deep golden brown.

Allow the cake to cool in the pan for 10 minutes before carefully turning it out onto a wire rack. Serve this rustic apple cake warm with a dusting of powdered sugar or a scoop of vanilla bean ice cream for the perfect comforting finish.