Step 1

Arrange a rack in the middle of the oven and heat the oven to 350ºF. Meanwhile, coat an 8-inch round cake pan with cooking spray or butter, then line the bottom with a parchment paper round. Melt 1 stick (8 tablespoons) unsalted butter. Peel, core, and dice 3 apples.

Step 2

Whisk 1 cup all-purpose flour, 1 teaspoon baking powder, and 1/4 teaspoon fine salt together in a medium bowl.

Step 3

Whisk 2 large eggs in a large bowl until fluffy. Add the melted butter, 3/4 cup packed light brown sugar, 1/4 cup spiced rum, and 1 teaspoon vanilla, and whisk to combine. Add the flour mixture and stir with a wooden spoon or rubber spatula until just combined. Add the apples and fold until just combined. Transfer the batter to the prepared pan and smooth the top.

Step 4

Bake until a toothpick inserted in the center comes out clean, about 40 minutes. Let cool for 15 minutes before carefully removing from pan (loosen the sides by running a thin knife around the edge if needed first). Dust with powdered sugar and serve.