These cookies owe their delicate texture to the combination of baking soda and cream of tartar, a version of homemade baking powder.
Adjust rack to lower third of oven and preheat oven to 325 degrees F. Line baking sheets with baking parchment. Sift flour with cinnamon, baking soda, cream of tartar, ginger, nutmeg, cloves, and salt. In a separate bowl, beat butter until creamy; gradually add confectioners’ sugar, then egg and vanilla, and continue beating until mixture is light. Stir in dry ingredients, incorporating thoroughly.
Using a ½-teaspoon measure, drop dough by rounded spoonfuls onto baking sheets and press a walnut half onto each cookie, flattening slightly. Bake for about 10 minutes, or until pale golden on the bottom.