Preheat the oven to 350. Line two baking sheets with parchment or silicone and set aside.

In a large bowl or the bowl of a stand mixer, beat together the cream cheese and butter until light and fluffy. Add the sugar, eggs, vanilla, and peppermint extract, and mix until combined. Add the flour, baking powder, and salt, and mix until combined.

Scoop the dough onto the prepared baking sheets, making scoops that are approximately 1 1/2 tablespoons each. Bake 11-13 minutes, or until lightly browned on the bottom. Remove and let cool completely.

When the cookies have cooled, whisk together the melted butter and powdered sugar. Add the peppermint extract and red food coloring, and mix to combine. Add enough milk to thin the glaze to a drizzling consistency. Drizzle the glaze over the cooled cookies and sprinkle with the crushed candy cane.