Eggnog Snickerdoodle Sandwich Cookies with Cinnamon and Nutmeg

Ingredients

• 1/2 cup (1 stick) unsalted butter, softened
• 3/4 cup granulated sugar
• 1 large egg
• 1 teaspoon vanilla extract
• 1 1/2 cups all-purpose flour
• 1/2 teaspoon cream of tartar
• 1/2 teaspoon baking soda
• 1/4 teaspoon salt
• 3 tablespoons cinnamon sugar, for rolling
• 1 1/2 cups powdered sugar
• 2-3 tablespoons eggnog, or more as needed
• 1/8 teaspoon ground nutmeg
• Pinch of salt