Preheat oven to 350 degrees. Spray a 10-cup bundt pan with cooking spray and set aside.
In a saucepan over medium-high heat, bring the diced apple and apple cider to a boil. Reduce heat to low and simmer for 15 - 20 minutes until the apple is soft and the cider is absorbed.
Remove from heat and mash with a fork to eliminate any big chunks.
Add the melted butter, buttermilk and vanilla bean paste to the saucepan with the apple mixture. Whisk to combine.
In a medium bowl, add the cake flour, baking powder, baking soda, salt, cinnamon, nutmeg and allspice. Mix to combine.
In the bowl of a standing mixer, beat the room temperature butter, dark brown sugar and caster sugar, at medium speed, until light and fluffy.
Add each egg one at a time and beat until combined, scraping down the sides as needed.
Reduce standing mixer speed to low. Alternate adding the dry ingredients and apple mixture to the standing mixer, beating until just combined.
Transfer the batter to the prepared bundt pan. Bake for 35 - 40 minutes until a tester comes out clean. Cool in the pan for 15 minutes then gently remove the cake from the pan.
To garnish, combine the granulated sugar, cinnamon and nutmeg and sprinkle all over the hot cake. Serve while still warm.