Step 1

Set an oven rack in the middle position.

Step 2

Preheat the oven to 350 degrees F.

Step 3

Grease a 9-inch springform or regular cake pan with the extra butter or nonstick cooking spray. If using a regular pan, line the bottom with parchment paper and grease it well.

Step 4

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

Step 5

Using a handheld mixer or a stand mixer with a paddle attachment, cream the remaining 1 stick of the butter and 2/3 cup of the granulated sugar together until light and fluffy, about 3 minutes.

Step 6

Add the eggs, one at a time, to the butter mixture, beating well and scraping down the sides of the bowl after each addition.

Step 7

Beat the vanilla and the rum into the butter mixture.

Step 8

Add the flour mixture and mix on low speed until just combined.

Step 9

Using a rubber spatula, fold in the apples.

Step 10

Pour the batter into the prepared pan, spreading the top until even.

Step 11

Sprinkle the remaining granulated sugar evenly over the top of the cake.

Step 12

Bake until the cake is golden and a toothpick inserted into the center comes out clean, about 40 minutes.

Step 13

Allow the cake to cool in the pan on a rack.

Step 14

Run a blunt knife around the edges of the cake and (if using a springform pan) remove the sides. If using a regular pan, carefully invert the cake onto the rack and gently flip the cake over onto a platter.

Step 15

Using a fine sieve, dust the top of the cake with the confectioners' sugar.

Step 16

Serve.