Preheat oven to 350 degrees F (175 degrees C). Line a rimmed baking sheet with a silicone mat or parchment paper.
Place flour, salt, baking soda, and cream of tartar in a mixing bowl. Add cinnamon, ginger, allspice, clove, and nutmeg. Whisk until thoroughly mixed, 1 or 2 minutes.
Place butter, sugar, and brown sugar in a separate mixing bowl. Cream together with a spatula or wooden spoon until mixture is smooth, 2 or 3 minutes. Add vanilla and egg. Stir until thoroughly combined.
Pour flour mixture into butter mixture. Stir until just combined or until the flour disappears.
Wrap bowl in plastic wrap. Chill dough in refrigerator for about 1 hour.
Stir cinnamon and sugar together in a shallow bowl or plate.
Scoop dough into 2 tablespoon balls. Roll in cinnamon-sugar mixture to coat all sides. Roll into smooth ball and place on prepared baking sheet, 3 to 4 inches apart. Flatten slightly.
Bake in preheated oven until browned, 10 to 12 minutes.
Cool on baking sheet 5 minutes; sprinkle with additional cinnamon-sugar mixture, if desired. Transfer cookies to cooling rack to cool completely.
If you’d like to add a bit of a shine to your cookies, you can brush them with a simple glaze. Mix confectioners’ sugar with milk or lemon juice to achieve brushing consistency. Brush onto cookies. Sprinkle with more cinnamon sugar or pumpkin pie spice, if desired.
1 1/2 cups flour, if weighed, should equal 6 1/2 ounces. If using fine salt instead of kosher, reduce to 1/4 teaspoon.
You can add a few pinches of the pumpkin spices to the rolling sugar, if desired.
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