Make the Cookie Dough

1. Combine Dry Ingredients: In a medium bowl, whisk together flour, baking soda, baking powder, and salt. Set aside.
2. Cream Butter and Sugar: In a large mixing bowl, cream the softened butter and granulated sugar until light and fluffy.
3. Add Egg and Extracts: Beat in the egg, vanilla extract, and peppermint extract until fully combined.
4. Incorporate Dry Ingredients: Gradually add the dry ingredient mixture to the wet ingredients, mixing until just combined. Avoid overmixing.
5. Chill the Dough: Cover the dough with plastic wrap and chill in the refrigerator for about 30 minutes. This helps the cookies hold their shape during baking.

Bake the Cookies

1. Preheat the Oven: Preheat your oven to 375°F (190°C) and line baking sheets with parchment paper.
2. Form Cookies: Scoop tablespoons of dough and roll them into balls. Place them on the prepared baking sheets, spaced about 2 inches apart.
3. Flatten Slightly: Gently press each cookie ball down with the bottom of a glass or your palm to flatten slightly.
4. Bake: Bake the cookies for 10-12 minutes or until the edges are lightly golden. The centers may look soft but will set as they cool.
5. Cool Completely: Remove from the oven and let the cookies cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.

Prepare the Icing

1. Mix Icing Ingredients: In a small bowl, whisk together powdered sugar, milk, and vanilla extract until smooth and creamy. Add more milk as needed to achieve desired consistency.
2. Decorate Cookies: Once the cookies are completely cool, drizzle the icing over the top using a spoon or piping bag.
3. Add Toppings: Immediately sprinkle crushed candy canes on top of the icing for a festive touch.