Step 1

In a stand mixer fitted with the paddle attachment, cream the granulated sugar, butter, and shortening on medium-high speed for 3 minutes, until very light and fluffy. Add the vanilla, salt, and egg and mix well. Gradually add the cake flour, scraping down the bowl once or twice, and mix to make a stiff dough.

Step 2

On a floured work surface, form the dough into two logs 1½ inches in diameter, rolling them firmly into a perfectly round shape. Wrap the logs in plastic wrap or waxed paper and chill for 2 hours or up to 1 week.

Step 3

When ready to bake, preheat the oven to 375ºF. Line two baking sheets with parchment paper.

Step 4

Cut the logs crosswise into ¼-inch-thick slices and place 1½ inches apart on the prepared baking sheets. Bake for 8 to 10 minutes, until the cookies are firm and the bottoms are a light golden brown. Sprinkle with the Demerara sugar, sugar sprinkles, or ground nuts.

Step 5

Cool on the baking sheets set on wire racks for 2 minutes, then transfer the cookies to the racks to cool completely.

Step 6

Store the cookies in an airtight container at room temperature for up to 5 days until ready to serve.