Preheat the oven to 350°F (180°C) and line two baking sheets with parchment paper.
Add the butter and sugar to the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed until well blended, about 1 minute, then scrape down the sides and bottom of the bowl.
Add the egg and peppermint extract, mix well, and scrape down the bowl again.
Sift in the flour, then add the baking soda and salt. Mix on low speed until a clumpy dough forms that clears the sides of the bowl.
Divide the dough into 24 portions (approximately 24 g each) and roll each into a smooth ball between your hands.
Place 12 dough balls on each baking sheet, spacing them about two inches apart.
Bake for 12 to 14 minutes, or until pale gold on the bottom. Cool on the baking sheets for 10 minutes, then move to a wire rack to cool completely.
Once the cookies have cooled, make the glaze. Sift the icing sugar into a shallow bowl. Add the corn syrup, salt, and 1 teaspoon of milk. Stir well, then continue adding milk, ½ teaspoon at a time, until the glaze is thick yet runs smoothly from the end of a spoon without clumping.
Dip the cooled cookies, top sides down, into the glaze. Let the excess drip off, then return them, right side up, to the rack. Sprinkle immediately with crushed candy canes while the glaze is still wet, then let the cookies set for a few hours until the glaze hardens.
Notes
For detailed ingredient notes, substitution tips, variations, and step-by-step photos, scroll through the full recipe post.
Use a digital kitchen scale for precise measurements and an oven thermometer to confirm your oven is heating correctly.
The cookies will be quite puffy when they come out of the oven, however they will deflate and crack. This is normal.
If the glaze thickens while decorating, stir in a few drops of milk to loosen it.
Don't glaze warm cookies or the glaze will just melt.
I buy crushed candy canes at the bulk store, but you can also place unwrapped candy canes in a zip-top bag and crush them with a rolling pin.
You can spoon or drizzle the icing on top of the cookies instead of dipping the tops.
Storage
Store glazed cookies in a single layer, or with parchment between layers, in an airtight container for up to four days at room temperature or one month in the freezer. You can also freeze unglazed cookies in a sealed container and glaze them after thawing.