Pour the apple cider into a small saucepan. Bring to a gentle simmer over medium heat and cook until reduced from 1 cup to ½ cup, about 10–15 minutes.
Remove from the heat and allow the reduced cider to cool to room temperature.
Preheat the oven to 375°F (190°C). Line a 12-cup muffin pan with paper liners or lightly grease the pan.
In a medium bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In a separate large bowl, beat the softened butter and sugar for 2–3 minutes, until light and fluffy.
Add the eggs one at a time, mixing well after each addition.
Stir in the vanilla extract.
Gradually mix in the cooled reduced apple cider.
Add the dry ingredients and gently mix until just combined. Do not overmix.
Fold in the finely diced apple.
Divide the batter evenly among the muffin cups, filling each approximately ¾ full.
Combine the granulated sugar and cinnamon for the topping.
Lightly brush the tops of the muffins with melted butter and sprinkle generously with the cinnamon-sugar mixture.
Bake for 18–22 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.
Cool the muffins in the pan for about 5 minutes, then transfer them to a wire rack.
Serve warm or allow them to cool completely before storing.