In a small saucepan, add 2 cups apple cider and 1 cinnamon stick. Bring to a boil, then reduce to a steady simmer for 25 minutes, stirring occasionally, until it reduces to ½ cup.
In a large mixing bowl, whisk together flour, baking powder, salt, cinnamon, and nutmeg.
In a stand mixer, beat room temperature butter, dark brown sugar, and granulated sugar on medium speed until light and fluffy. Add eggs one at a time, then the vanilla.
Pour the dry ingredients into the wet ingredients. Mix on low just until combined. With the mixer running, drizzle in the ½ cup reduced apple cider until batter is smooth.
Scoop batter into a regular-sized muffin pan lined with paper liners or greased with non-stick spray, filling each cup ⅔ full. Liners are not needed if you are using a silicone muffin pan. Bake at 350°F (180°C) for 15 - 20 minutes, or until a toothpick comes out clean. Transfer muffins to a cooling rack.
While muffins are cooling, melt 6 tbsp of butter and set aside. In a separate bowl, combine ½ cup granulated sugar and 1 tsp of ground cinnamon, set aside. Brush or roll warm muffin tops with melted butter, then roll in the cinnamon sugar mixture until fully coated - like true apple cider donuts. Enjoy!