Preheat the Oven: Start by preheating your oven to 350°F (175°C) to ensure that your cookies bake evenly.
Mix Dry Ingredients: In a medium bowl, whisk together 2 ½ cups of all-purpose flour, 1 teaspoon of baking soda, and ½ teaspoon of salt. Set this mixture aside.
Cream Butter and Sugar: In a large mixing bowl, cream together 1 cup of softened unsalted butter and 1 cup of granulated sugar until the mixture is light and fluffy. This should take about 3-4 minutes.
Add Egg and Extracts: Beat in 1 large egg, 1 teaspoon of vanilla extract, and 1 teaspoon of peppermint extract until fully incorporated.
Combine Mixtures: Gradually add the dry ingredients to the wet mixture, mixing just until combined. Avoid over-mixing to keep the cookies soft.
Shape the Cookies: Using a tablespoon or a cookie scoop, drop rounded balls of dough onto a baking sheet lined with parchment paper, spacing them about 2 inches apart.
Bake: Bake the cookies in the preheated oven for 8-10 minutes, or until the edges are lightly golden. You want the centers to remain soft.
Cool the Cookies: Remove the cookies from the oven and allow them to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.
Prepare the Buttercream: For the frosting, beat 1 cup of softened unsalted butter in a mixing bowl until creamy. Gradually add 4 cups of powdered sugar, mixing on low speed until fully blended.
Flavor the Frosting: Add 2 tablespoons of milk, 1 teaspoon of vanilla extract, and 1 teaspoon of peppermint extract. Beat on high until the frosting is light and fluffy, about 3-5 minutes.
Frost the Cookies: Once the cookies are completely cool, use a knife or a piping bag to generously frost each cookie with the buttercream.
Garnish: Finally, sprinkle the frosted cookies with crushed candy canes for a festive touch.