Preheat the oven to 350°F.
In a large bowl, mix the diced apples with the vanilla and beaten eggs until combined.
Add the sugar, cinnamon, cardamom, ginger, and melted butter. Stir until well mixed.
Add the flour, salt, and baking soda. Stir until just combined.
Grease a 9-inch cake pan and pour in the batter, spreading it evenly with a spatula.
Top the batter with the prepared crumble.
Bake for 60-80 minutes, or until a toothpick inserted into the center comes out clean. Start checking at around 55 minutes, as baking times may vary by oven.