Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a mixing bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
In another bowl, cream together the softened butter and granulated sugar using an electric mixer on medium speed until light and fluffy.
Beat in the egg, vanilla extract, and peppermint extract until well combined.
Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Roll out the dough on a floured surface to about ¼ inch thick. Use the tree-shaped cookie cutter to cut trees out of the dough and place them on the prepared baking sheet.
Bake in the preheated oven for 8-10 minutes, or until the edges are lightly golden. Let them cool on a cooling rack.
While the cookies are cooling, prepare the frosting by mixing powdered sugar with 2 tablespoons of milk, adding more milk as needed to reach a spreadable consistency. Add green food coloring to achieve your desired shade.
Once the cookies are cool, use a spatula to frost the trees with green icing.
Decorate the trees with crushed peppermint candies, and top each with a star-shaped sprinkle or edible glitter.