Combine shortening and 1/2 cup sugar in a bowl; cut with a pastry knife until crumbly. Add egg and vanilla; beat with an electric mixer until well combined. Work in 2 cups flour with your hands; knead until stiff and similar in consistency to pie dough.

Preheat the oven to 300°F (150°C). Line baking sheets with parchment or Silpat® mats.

Dust a work surface with flour. Roll dough to 1/8-inch thickness. Use a cookie cutter to cut rounds; create matching cut-out cookies for tops. Re-roll and repeat until all dough is used.

Transfer cookies to prepared baking sheets. Bake for 10 minutes, ensuring they do not brown. Remove and cool completely before handling.