Reduce the cider. In a small saucepan, simmer apple cider over medium heat until reduced to 1/2 cup, about 10 to 15 minutes. Cool for 5 minutes.
Prep. Heat oven to 375F. Line a 12-cup muffin pan with liners or grease well.
Mix dry ingredients. In a bowl, whisk flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
Mix wet ingredients. In a separate bowl, whisk eggs, brown sugar, granulated sugar, melted butter, milk, vanilla, and the reduced cider.
Combine. Add wet to dry and stir gently until just combined. Do not overmix.
Bake. Divide batter into muffin cups (about 3/4 full). Bake 16 to 19 minutes, until a toothpick comes out clean or with a few moist crumbs.
Coat. Cool muffins 5 minutes. Mix sugar, cinnamon, and salt in a bowl. Brush or dip warm muffins in melted butter, then roll in cinnamon sugar. Repeat for a thicker coating if you want.