1. Preheat the oven to 350°F and line two baking sheets with parchment paper.

2. In a large bowl, beat the softened butter and 1 1/4 cups granulated sugar until light and fluffy.

3. Mix in the egg, vanilla extract, and peppermint extract until smooth.

4. In a separate bowl, whisk together the flour, baking soda, and salt.

5. Gradually add the dry ingredients to the wet ingredients and mix just until a soft dough forms.

6. Scoop the dough into tablespoon-sized portions and roll each one into a ball.

7. Roll each dough ball in the remaining 1/4 cup granulated sugar.

8. Place the dough balls on the prepared baking sheets about 2 inches apart.

9. Gently press the tops slightly and sprinkle crushed peppermint candies over each cookie.

10. Bake for 9 to 11 minutes, until the edges are set and the centers still look soft.

11. Let the cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.