Step 1: Simmer the 2 cups of apple cider in a small saucepan over medium heat for 15-20 minutes until it reduces to exactly 1/2 cup. Set aside to cool.
Step 2: Preheat your oven to 350°F (175°C) and grease a 12-cup muffin tin or line with paper liners.
Step 3: In a medium bowl, whisk together the flour, baking powder, baking soda, salt, 2 tsp cinnamon, and nutmeg.
Step 4: In a large bowl, cream together the softened butter, 1/2 cup granulated sugar, and brown sugar until light and fluffy.
Step 5: Beat in the eggs one at a time, then stir in the vanilla extract and the cooled, reduced apple cider.
Step 6: Gradually add the dry ingredients to the wet ingredients, stirring just until combined. Do not overmix.
Step 7: Divide the batter evenly among the muffin cups and bake for 18-22 minutes, or until a toothpick inserted into the center comes out clean.
Step 8: While muffins are cooling slightly, melt the remaining 1/2 cup of butter and prepare the cinnamon-sugar mixture in a separate bowl.
Step 9: Dip the tops (or the whole muffin) into the melted butter, then roll generously in the cinnamon-sugar mixture.