Preheat oven to 350 degrees F. Prepare a 9" springform pan with cooking spray.
cooking spray
In a large mixing bowl, cream together butter and granulated sugar until fluffy; about 2 minutes.
1/2 cup unsalted butter, softened, 3/4 cup granulated sugar
Add eggs, rum extract and sour cream; blend until smooth.
2 large eggs, 1 tsp rum extract , 1/2 cup sour cream
In a medium bowl, whisk together flour, baking powder and salt.
1-3/4 cups all-purpose flour, 2-1/2 tsps baking powder, 1/4 tsp table salt
Pour flour mixture into wet ingredients in 2 or 3 increments and blend well (but do not overmix) with a rubber spatula. (Batter will be very thick.)
Pour batter into prepared pan, spreading as evenly as possible. (It will seem there is not enough batter, but it rises a lot during the baking process.)
Toss apples with brown sugar and cinnamon until coated. Arrange apples in a spiral design, overlapping from the center out.
2 apples, peeled and sliced thinly (Granny Smith or Honeycrisp work well), 2 tbsp light brown sugar, 1/2 tsp ground cinnamon
Bake for 50 minutes or until a toothpick comes out clean. (Do not overbake.)
Cool completely before removing from pan to a serving dish. Dust with confectioners' sugar.
1 tbsp confectioners' sugar
Serve with whipped cream or ice cream.
whipped cream or ice cream