Preheat your oven to 350°F (175°C) and generously grease a standard 12-cup muffin tin with butter or non-stick cooking spray.
In a medium bowl, whisk together the all-purpose flour, baking powder, 1 teaspoon cinnamon, salt, and nutmeg until they are fully combined and uniform in color.
In a separate large bowl, use an electric mixer on medium speed to beat the 1/2 cup of softened butter with the 1/2 cup granulated sugar and 1/2 cup brown sugar for 2-3 minutes, until the mixture becomes light and fluffy.
Beat the eggs into the butter-sugar mixture one at a time, followed by the vanilla extract, scraping down the sides of the bowl as needed to ensure everything is incorporated.
With the mixer on low speed, alternate adding the dry ingredients with the apple cider and buttermilk, beginning and ending with the dry ingredients, and mix just until the batter is smooth with no visible streaks of flour.
Evenly divide the batter among the 12 prepared muffin cups, filling each about 2/3 full, and bake for 18-22 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
While the muffins bake, prepare the topping by stirring together the 1/2 cup granulated sugar and 1 teaspoon cinnamon in a small, shallow bowl, and place the 4 tablespoons of melted butter in a separate bowl.
Allow the muffins to cool in the pan for 5 minutes, then carefully dip the top of each warm muffin first into the melted butter and then into the cinnamon-sugar mixture, coating the top completely.