Peel and core the apples and cut them lengthwise into eight equal wedges. Place the apple into a pot. To make the compote, add the raw sugar and granulated sugar and lightly toss to coat. Turn on the burner. Cover and cook on medium low heat.
When the melted sugar begins to make a simmering sound, uncover and shake the pot up and down to bring the bottom of the apple to the top. This method will help to avoid breaking the shape of the apple. Occasionally mix the apple from the bottom with a wooden paddle.
After about 10 minutes, the juices should come out of the apple. Make cuts in an X pattern in the center of a clean paper towel and place it onto the apple. This is a substitute for a drop-lid, which help the ingredient cook evenly. Then, simmer for 10 more minutes.
When the apple begins to turn translucent, remove the paper towel. Continue reducing the juices without a lid. While the juices still remain, add the raisins, lemon juice and cinnamon powder.
Gently mix the ingredients. Reduce the juices until there is only a small amount on the bottom. Turn off the burner and let it sit to cool.
Now, let's make the almond cream. In a fine mesh strainer, combine the almond powder, raw sugar and cake flour. Sieve the powder into a bowl. Be sure to bring all the ingredients to room temperature beforehand.
The unsalted butter should be at room temperature also and softened in a bowl. Add the sifted powder to the butter. Combine the mixture with a spatula.
When the butter is evenly incorporated, switch to a balloon whisk. Add the beaten egg a little at a time and combine the mixture. Gradually adding the egg will help to avoid separation. Now, the almond cream is ready.
Let's fill the tart crust. Place the almond cream onto the bottom of the crust. Spread it with a spatula evenly.
Arrange the apple compote in concentric circles over the cream. The apples should slightly overlap each other. Cut the remaining apple wedges in half and fill the middle of the tart with them. Distribute the raisins on top. Gently press the apple to even out the surface.
Preheat the oven to 190 °C (374 °F) and place the tart pan into it. Bake the tart at 190 °C (374 °F) for 40 to 50 minutes. To help brown the tart evenly, rotate the pan while baking. If the surface begins to burn too quickly, cover the tart with aluminum foil to adjust the color.
When the almond cream and apple turn golden brown, it is ready. Remove and place the pan onto a cooling rack.
Let's make the glaze. Add the rum to the apricot jam and stir to mix. You can also use hot water instead of the rum. Brush the apricot glaze over the top. Let it sit to cool and then remove the tart pan.
Be sure to use apples that have a firm texture for baking. In Japan, Tsugaru and Fuji are the most popular brands for baking apples.
Alternatively, you can use other fruit such as peaches, European pears and figs.