In a large bowl beat the sugar, cream cheese, and butter with an electric mixer on medium speed until combined. Beat in the egg, vanilla, and peppermint extract. Stir in the flour, baking powder, and salt to make a soft dough. Take half the dough out of the bowl and wrap in plastic wrap. Blend the red food coloring into the dough remaining in the bowl. Wrap in plastic wrap. Refrigerate the dough at least 2 hours or overnight.
Preheat the oven to 375°F and line 2 baking sheets with parchment paper. Put the peppermint candies in a zip-top plastic bag and crush them into crumbs with a rolling pin or the bottom of a heavy skillet.
To make each cookie, take a teaspoon each of red and white dough, and use your palms to roll each piece into a 5- to 6-inch rope. Gently twist together the red and white ropes, place on the baking sheet and curve the top over like a candy cane. Repeat with the remaining dough.
Bake 8 to 10 minutes, until they just begin to set. Do not let the cookies brown. Remove from the oven and immediately sprinkle each cookie with a little of the crushed peppermints. Let cool for 5 minutes on the baking sheet, then transfer to a wire rack to cool completely.