Step 1In the bowl of a stand mixer, or in a large bowl using an electric mixer, cream together the butter and powdered sugar. Beat in the egg, then the vanilla.
Step 2Beat in the cream of tartar, then slowly beat in the flour until incorporated. Gently stir in the pecans, candied red and green cherries and candied orange peel until evenly incorporated using a spoon or spatula. The dough will be sticky.
Step 3Roll the dough into logs approximately 1 1/2 inches thick. Roll the logs in parchment or wax paper and freeze until very firm, several hours to overnight.
Step 4Heat the oven to 375 degrees. Cut the dough into rounds one-fourth-inch thick. Bake the cookies on a greased baking sheet until cooked through (the cookies will be pale with light golden-brown edges), 6 to 8 minutes.
Step 5Store the cookies in an airtight container. The cookies can be made up to 2 months ahead and frozen; thaw before serving.