Preheat the oven to 350°F. Spray a 9-inch springform or regular cake pan with nonstick cooking spray.

In a small bowl, whisk together the flour, baking powder and salt.

In a stand mixer with the paddle attachment, cream the butter and granulated sugar until light and fluffy, about 3 minutes. Add the eggs, one at a time, beating well and scraping down the sides of the bowl after each addition. Beat in the vanilla and rum. Don't worry if the batter looks grainy. Add the flour mixture and mix on low speed until just combined. Using a rubber spatula, fold in the chopped apples.

Pour the batter into the prepared pan and sprinkle evenly with 1 tablespoon of granulated sugar. Bake for about 40 minutes, or until the cake is lightly golden and a toothpick inserted into the center comes out clean. Allow the cake to cool until just warm. Run a blunt knife around the edges of the cake and remove the sides of the springform pan if using. Using a fine sieve, dust with Confectioners' sugar (if using).

Cake can be served warm or room temperature, with or without lightly sweetened whipped cream or vanilla ice cream.