Center the oven rack and preheat the oven to 350F (180 C).
Butter a 9″ x 13 ” (13 cm x 33 cm) rectangular mold.
Line the mold with parchment paper, then butter again and flour.
Remove excess flour and place the mold on a baking sheet.

Combine flour, baking powder, baking soda, spices, and salt.

In a saucepan, melt the butter over low heat.
Add the brown sugar and mix with a whisk until the mixture is smooth, about 1 minute.
Remove the saucepan from the heat.

Still in the saucepan, add the eggs one by one, whisking between each addition.
Add the apple sauce, vanilla, and rum, and whisk until the ingredients are incorporated and the mixture is smooth.
Stir in the dry ingredients, then stir in the apple, raisins, and pistachios.
Pour the mixture into the prepared mold.

Bake in the oven for 23 to 25 minutes, or until the cake comes away from the edges and a knife inserted in the center comes out clean.
Transfer the mold to a wire rack and let the cake cool while you prepare the glaze.

Glaze:
In a small saucepan, whisk together the cream, sugar, butter, and corn syrup. Bring the mixture to a boil, stirring frequently.
Adjust the heat so that the glaze simmers.
Cook, stirring often, for 5 minutes.
Remove the saucepan from the heat and stir in the vanilla.

Unmold the cake onto a cutting board, then remove the parchment paper, and transfer the cake to a large serving plate.
Pour the glaze over the top and spread with a spatula.
Cut into 32 rectangles.