Preheat the oven to 350°F (175°C). Grease and flour an 8-inch (20 cm) round cake pan.
In a small bowl, toss the sliced apples with lemon juice to prevent browning. Set aside.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt.
In a large bowl, cream the softened butter and granulated sugar together until light and fluffy, about 3-4 minutes.
Add the eggs one at a time to the butter mixture, beating well after each addition.
Mix in the vanilla extract.
Alternately add the dry flour mixture and the milk to the butter mixture, beginning and ending with the flour mixture. Mix until just combined.
Gently fold the sliced apples into the batter.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
In a small bowl, combine the brown sugar and ground cinnamon. Sprinkle evenly over the top of the batter.
Bake for 35-40 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 before transferring it to a wire rack to cool completely.
Slice and serve the cake once cooled.