Preheat your oven to 350°F (175°C). Grease and flour a baking pan.
In a mixing bowl, whisk together the flour, baking powder, and salt.
In another bowl, beat the sugar and butter until light and fluffy. Add the eggs one at a time, then stir in the vanilla.
Gradually add the flour mixture to the butter mixture, mixing until just combined. Fold in the chopped apples.
Pour the batter into the prepared pan and bake for 45 minutes, or until a toothpick inserted into the center comes out clean.
For the glaze, combine the brown sugar, heavy cream, and butter in a saucepan over medium heat. Bring to a boil, stirring constantly. Remove from heat and stir in the vanilla.
Pour the glaze over the warm cake. Let it cool before serving.