Preheat oven to 375ºF and using some of melted butter, grease a 12 cavity donut pan or two 6 cavity donut pans. In a small saucepan, simmer the apple cider over medium heat until it has reduced to about 1/3 cup, this will take about 15 minutes. Set aside to cool.

In a batter bowl, stir together the flour, baking powder, baking soda, cinnamon, nutmeg and salt. In a separate bowl, whisk together the egg, brown sugar, remaining 2 Tbsp. melted butter, buttermilk, cooled apple cider reduction, and vanilla extract.

Pour the wet ingredients into the dry ingredients and fold together using a rubber spatula until just moistened. Spoon the batter into the greased donut pan filling each cavity about 2/3 full. Bake in the preheated oven for 10 to 15 minutes, or until donuts are risen and golden brown and a toothpick inserted in the center comes out clean. Remove donuts from oven and cool for 10 minutes, then remove them to a cooling rack and let cool for 30 minutes.

To prepare glaze: whisk together the powdered sugar, maple syurp, and vanilla extract until a thick glaze forms. It should be spreadable but not runny. Using a flexible spatula, frost each donut with about 1 Tablespoon of glaze.