Preheat oven to 375 degrees F (190 degrees C). Line baking sheets with parchment paper, and set aside.
Mix the flour, baking soda, and cream of tartar in a bowl. In another bowl, beat the butter and 1 1/2 cups confectioners' sugar together with an electric mixer until light and fluffy. Mix in orange extract, grated orange zest, and egg. Stir in the flour mixture, and blend well.
Drop teaspoon-sized portions of dough about 2 inches apart onto the parchment lined baking sheets. The cookies will spread out to about 1 1/2 inches when baked.
Bake in the preheated oven for 10 to 14 minutes, until the cookies are light brown. Remove from the oven, and sift remaining confectioners' sugar onto the hot cookies. Allow to cool, and store in an airtight container.
