Preheat the oven to 350°F (177°C) degrees, fill a muffin tin with cupcake liners, set aside.

In a medium mixing bowl, whisk together flour, brown sugar, apple pie spice, baking powder and salt, then set aside.

In a large mixing bowl, whisk together eggs, apple cider (or juice) and milk. Slowly add the dry ingredients until just incorporated. Fold in grated apples. Fill each cavity in the muffin tin 3⁄4 of the way with batter.

Bake in the oven at 350°F (177°C) for 20 minutes or until a knife comes out clean. Remove from the oven and allow to cool completely.

To make the frosting, beat together butter, powdered sugar, milk and cinnamon until smooth. Add additional powdered sugar to get the consistency desired.

Pipe on the frosting or use a knife to spread it on if preferred.