Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone mats to prevent sticking.

In a large mixing bowl, combine the softened cream cheese and butter. Beat on medium speed until the mixture becomes light and fluffy. Gradually add the granulated sugar and continue mixing until well incorporated.

Incorporate the eggs, one at a time, beating well after each addition. Add the vanilla and peppermint extracts, mixing until smooth and evenly blended.

Sift together the all-purpose flour, baking powder, and salt in a separate bowl. Gradually add this dry mixture to the wet ingredients, mixing on low speed until a cohesive dough forms. Avoid overmixing.

Using a cookie scoop or a tablespoon, portion the dough into 1½-tablespoon-sized mounds. Place them onto the prepared baking sheets, ensuring even spacing to allow for spreading.

Transfer the baking sheets to the preheated oven and bake for 11-13 minutes, or until the cookie bottoms are lightly golden. Remove from the oven and allow the cookies to cool completely on a wire rack.

In a small bowl, whisk together the melted butter and powdered sugar. Add the peppermint extract and a drop of red food coloring, mixing thoroughly. Gradually add milk, one teaspoon at a time, until the glaze reaches a drizzling consistency.

Once the cookies have cooled, drizzle the prepared glaze over the tops. Immediately sprinkle the crushed candy cane over the glaze before it sets. Allow the glaze to harden before serving or storing.