Preheat the oven.
Preheat your oven to 350°F. Grease a standard muffin pan or line it with paper muffin liners.
In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In a separate bowl, whisk together the egg, brown sugar, melted butter, apple cider, milk, and vanilla extract until combined.
Pour the wet ingredients into the dry ingredients and stir gently until just combined. Avoid overmixing so the muffins stay tender.
Divide the batter evenly among 10–12 muffin cups, filling each about two-thirds full.
Bake for 15–20 minutes, or until a toothpick inserted into the center comes out clean. Let the muffins cool in the pan for about 5 minutes before transferring them to a wire rack.
Mix the granulated sugar and cinnamon in a small bowl. Once the muffins are cool enough to handle, brush the tops lightly with melted butter and dip or sprinkle them with the cinnamon-sugar mixture.
Serve slightly warm with a cup of coffee, tea, or apple cider. The cinnamon-sugar topping gives these muffins that familiar apple cider donut feel without the extra work of making traditional donuts.