Set your oven to 350°F (175°C). Grease your 9-inch round cake pan with butter or non-stick spray, then lightly dust with flour or line with parchment paper to ensure easy removal.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, ground cinnamon, ground nutmeg, and salt.
In a large bowl, beat the softened butter and granulated sugar using an electric mixer or whisk until the mixture is light and fluffy—about 3 to 4 minutes.
Beat in the eggs one at a time, making sure each is fully incorporated before adding the next. Stir in the vanilla extract.
With the mixer on low, add the dry flour mixture in three parts, alternating with the apple cider in two parts. Begin and end with the dry ingredients. Mix just until combined.
Pour the batter into your prepared cake pan, smoothing the top with a spatula. Bake for 35 to 40 minutes until a toothpick inserted in the center comes out clean or with just a few moist crumbs.
While the cake is still warm but cool enough to handle, mix the additional 1/4 cup granulated sugar with 1 teaspoon cinnamon in a small bowl. Gently invert the cake onto a cooling rack and sprinkle or brush the cinnamon sugar mixture over the top and sides.
Let the cake cool completely before slicing. Serve with a hot cup of tea or coffee and enjoy the taste of fall in every bite.