Pour 2 cups of apple cider into a small saucepan and bring to a simmer over medium heat. Allow to reduce to ½ cup (about 15-20 minutes). The liquid will become darker, more concentrated, and syrupy. Cool completely before using.
Preheat your oven to 350°F (175°C). Generously grease a 10-inch bundt pan with butter or cooking spray, ensuring you reach all crevices. Dust the greased pan with flour and tap out the excess.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, allspice, and salt.
In a large bowl using an electric mixer, beat the butter and both sugars on medium-high speed until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition. Mix in the cooled reduced cider, buttermilk, and vanilla extract until just combined.
Gradually fold in the dry ingredients, mixing on low speed until just combined. Be careful not to overmix. Gently fold in the grated apple.
Pour the batter into the prepared bundt pan and smooth the top. Bake for 45-50 minutes, or until a toothpick inserted in the center comes out clean with just a few moist crumbs.
Allow the cake to cool in the pan for 10 minutes, then invert onto a cooling rack.
While still warm (but not hot), brush the entire cake with melted butter. In a shallow dish, mix the granulated sugar and cinnamon, then generously coat the buttered cake, pressing gently to adhere.