Place sliced apples in a microwave safe shallow bowl. Microwave in 1 minute intervals until softened, about 3 minutes, stirring in between. Toss with lemon juice and spiced rum, then set aside to cool for about 10 minutes.

Preheat oven to 325°F and butter a 9 inch springform pan lined with parchment paper or a silicone mat.

In a medium bowl, whisk together 1 cup flour, 1 cup 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 2 egg yolks to the remaining batter, then fold in the cooled apple slices. Pour the mixture into the prepared pan, gently pressing down the apples to create an even layer.

Add the remaining 2 tablespoons of flour to the reserved batter and whisk until smooth. Spoon it over the apple mixture, spreading evenly. Sprinkle with the remaining tablespoon of sugar.

Bake in the preheated oven for 1 hour to 1 hour 15 minutes until golden brown. Let cool on a wire rack, then remove from the pan and dust with powdered sugar before serving.

In a small saucepan over medium heat, combine milk, maple syrup, and ginger. Bring to a simmer, then remove from heat and let steep for 30 minutes.

Sieve out the ginger pieces and return to medium heat, bringing the milk back to a simmer.

In a small bowl, whisk the egg yolks. While whisking, slowly mix in a bit of warm milk to temper the eggs. Add the yolks and milk mixture back to the remaining milk.

Stirring constantly, cook the custard until it coats the back of a spoon. Remove from heat and add the vanilla and spiced rum. Pour into a heat-safe bowl and let cool before refrigerating until cold.