Pour the apple cider into a small saucepan. Bring to a gentle simmer over medium heat and cook for 15 to 20 minutes, until reduced to exactly 1/2 cup. Transfer to a heatproof measuring cup and cool for about 10 minutes.

Preheat the oven to 375°F (190°C). Lightly grease a standard 12-cup muffin pan.

In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.

In a large bowl, whisk together the 1/2 cup melted butter, brown sugar, and 1/4 cup granulated sugar until combined.

Whisk in the eggs, then add the sour cream, vanilla extract, and cooled 1/2 cup reduced apple cider. Whisk until combined.

Add the dry ingredients to the wet ingredients. Fold gently with a spatula just until no large streaks of flour remain. Do not overmix.

Divide the batter evenly among the 12 prepared muffin cups, filling each approximately three-quarters full.

Bake at 375°F (190°C) for 16 to 19 minutes, until the tops are risen and lightly golden. A toothpick inserted into the center should come out clean or with a few moist crumbs.

Cool the muffins in the pan for 5 minutes, then carefully transfer them to a wire rack.

Combine the 1/2 cup granulated sugar and 1 1/2 teaspoons cinnamon in a shallow bowl. Keep the 4 tablespoons melted butter in a separate bowl.

While the muffins are still warm, lightly brush the tops and sides with melted butter. Roll or generously coat each muffin in the cinnamon-sugar mixture.

Let the coated muffins rest for about 10 minutes before serving.