Preheat your oven to 350°F (175°C). Grease a 9-inch round cake pan with butter or non-stick spray and lightly dust it with flour, or line it with parchment paper for easy removal.
In a large bowl, sift together 2 cups of all-purpose flour, 1 teaspoon baking powder, 1 teaspoon baking soda, 1 teaspoon ground cinnamon, ½ teaspoon ground nutmeg, and ½ teaspoon salt. Set aside.
In a separate bowl, beat ½ cup softened unsalted butter, 1 cup granulated sugar, and ½ cup brown sugar until the mixture is light and fluffy—about 3 to 4 minutes with an electric mixer.
Beat in 2 large eggs one at a time, ensuring each is fully incorporated before adding the next. Then mix in 1 teaspoon vanilla extract.
Gradually add the dry ingredient mixture to the wet ingredients, alternating with 1 cup of apple cider. Begin and end with the dry ingredients, mixing gently to combine but being careful not to overmix.
Pour the batter into your prepared cake pan and smooth the top with a spatula. Bake for about 35-40 minutes, or until a toothpick inserted into the center comes out clean.
While the cake bakes, mix together ¼ cup granulated sugar and 1 teaspoon ground cinnamon in a small bowl. Once the cake is out of the oven and still warm, brush the top lightly with melted butter (optional), then sprinkle the cinnamon sugar mixture generously over the surface.
Allow the cake to cool in the pan for 15 minutes before transferring it to a wire rack to cool completely. Slice, serve, and enjoy.