• Preheat oven to 375°F. Grease 12-count muffin tin or line with paper liners.

Muffins:

• In a large bowl combine flour, baking powder, salt, and cinnamon. Set aside.
• Using a hand mixer or a stand mixer fitted with the paddle attachment, beat butter, granulated sugar and brown sugar until creamy and combined, about 2 minutes. Add the eggs and vanilla, beating until combined and scraping the sides and bottom of the bowl as needed. Add half the dry ingredients, beating until just combined. Add the cider/milk, beating until combined, then beat in the remaining flour. Using a rubber spatula or wooden spoon stir in the grated apples (leaving out any excess juice that accumulated when grating the apples).
• Scoop the dough into the prepared muffin tin, filling each cup almost all the way to the top. I use an ice cream scoop for this.

Topping:

• Combine the granulated sugar and cinnamon for the topping, then sprinkle it on top of each muffin.
• Bake for 22-26 minutes, until a toothpick inserted into the center comes out without raw batter on it. Place the pan on a wire rack to cool for 10 minutes then remove the muffins from the pan and place directly on the rack to finish cooling. Once cool, add icing (if using).

Icing:

• Whisk all ingredients until smooth, increasing the milk 1 teaspoon at a time until you reach your desired consistency. Adjust the consistency by adding more powdered sugar (to thicken) or more milk (to thin). Use a small spoon to drizzle icing over the tops of the cooled muffins.