Place sliced apples in a microwave safe shallow bowl. Microwave in 1 minute intervals until softened, about 3 minutes.

Stir apples between intervals and once pliable, toss with lemon juice and spiced rum. Set aside to cool, about 10 minutes.

Preheat the oven to 325°F. Butter a 9-inch springform pan and place it on a baking sheet lined with parchment.

In a medium bowl, whisk together 1 cup of flour, 1 cup of sugar, baking powder, and salt.

In a large bowl, mix together the egg, milk, oil, and vanilla. Gradually add dry ingredients until just moistened. Reserve 1 cup of batter.

Whisk in the 2 egg yolks to the remaining batter and fold in cooled apple slices.

Pour the apple mixture into the prepared pan and press apples down evenly.

Add remaining 2 tablespoons of flour to reserved batter and whisk until smooth. Spoon over apple mixture.

Sprinkle remaining 1 tablespoon of sugar over top. Bake for 1 hour to 1 hour 15 minutes until golden brown.

Let cool on a wire rack. Dust with powdered sugar before serving.

In a saucepan, combine whole milk, maple syrup, and sliced ginger. Heat until hot but not boiling.

In a bowl, whisk together egg yolks and spiced rum.

Slowly pour hot milk mixture into the yolk mixture, whisking continuously. Return to saucepan.

Cook over low heat until thickened. Stir in vanilla bean paste. Serve warm over cake.