Preheat the oven to 350°F (180°C) and grease an 8 or 9-inch cake pan or line with parchment paper. Set aside.
Prepare the apples: Peel the apples, and chop them into ½ inch pieces. Mix the apples with brown sugar and cinnamon, and set aside.
Whisk the flour and baking powder. Set aside.
In a medium-sized mixing bowl, beat sugar with oil, then beat in eggs, milk, and vanilla extract.
Pour the dry ingredients over the wet ingredients, and gently whisk until just combined. Make sure not to overmix the batter.
Fold in the cinnamon apples, and pour the batter evenly into the prepared cake pan.
Bake: Bake for 30-35 minutes. Baking times vary, so keep an eye on yours. The cake is done when a toothpick inserted in the center comes out clean.
Remove the cake from the oven, and set on a wire rack to cool down. Allow to slightly cool for at least 30 minutes before slicing and serving.