Begin by preheating your oven to 350°F. Line two large baking sheets with parchment paper and set them aside.
In a large mixing bowl, cream together ¾ cup unsalted butter and ½ cup brown sugar using an electric mixer on medium-high speed. Beat until the mixture is light and fluffy, which should take about 2 to 3 minutes.
Add in 1 large egg and 1 teaspoon vanilla extract to the buttery mixture. Beat until fully combined and smooth.
In a separate bowl, whisk together 2 cups all-purpose flour, 1 teaspoon baking soda, ½ teaspoon salt, 1 teaspoon ground cinnamon, ¼ teaspoon ground ginger, and ⅛ teaspoon nutmeg. This dry mix is crucial for ensuring that the spices are evenly distributed throughout the dough.
Gradually stir one-third of the dry mixture into the wet mixture on medium-low speed until just combined. Next, add half of the ½ cup maple syrup and continue to mix. Follow this by adding another third of the flour mixture and then the remaining maple syrup. Finally, fold in the last third of the flour mixture, stirring just until everything is incorporated.
Once the dough is ready, stir in 1 ½ cups grated apple until evenly distributed.
Using a medium cookie scoop, drop the cookie batter onto the lined baking sheets, spacing them about 2 inches apart.
Bake the cookies for 12 to 14 minutes, or until they are turning light golden brown. Keep an eye on them; you want to avoid over-baking, as they’ll continue to firm up as they cool.
Once baked, let the cookies rest on the baking sheet for about 5 minutes before carefully transferring them to a cooling rack to cool completely.
While the cookies are cooling, prepare the icing. In a small bowl, whisk together 1 cup powdered sugar, 1 tablespoon heavy whipping cream, 1 tablespoon melted butter, and 1 teaspoon maple syrup until the mixture is smooth.
For the final touch, transfer the icing to a resealable plastic bag and cut off a small corner. Pipe the icing onto the cooled cookies or spread it with an offset spatula for a more rustic look.