Prepare spiced cider reduction: In a large saucepan, heat apple cider with cinnamon, cloves, allspice, and ginger over medium-high heat, simmering the mixture until it reduces to 2 cups, which takes just under 30 minutes on my stove. Stir occasionally. Bask in the otherworldly aroma.
Make the batter: Heat your oven to 350°F. Line the bottom of a 9-inch round or 8-inch square cake pan with parchment paper and coat the sides with nonstick cooking spray. In a large bowl, combine flour, baking soda, and kosher salt. Make a well in the middle and pour in oil, brown sugar, cider vinegar, and 1 3/4 cups of the reduced cider (reserving the remaining 1/4 cup for the glaze). Whisk to combine until no lumps remain. Pour into the prepared pan.
Bake the cake: For 30 to 35 minutes, or until the top is springy and a toothpick inserted in the center comes out with just a few sticky crumbs (but not wet or loose batter). Cool the cake in the pan on a wire rack for 10 minutes, then cut around it with a knife to ensure it is loosened and flip it out onto a plate.
Finish the cake: Place powdered sugar in a medium bowl and stir in 3 tablespoons of the remaining spiced apple cider reduction, whisking until a thick glaze forms. Add some or all of the remaining 1 tablespoon reduction if needed to get your desired consistency. Pour the glaze over the center of the cake and use a spatula to gently trickle it down the sides.
Go ahead, eat the cake while it’s still warm. Do ahead: This cake keeps at room temperature loosely covered for 2 to 3 days and up to a week in the fridge.