Line two sheet pans with parchment paper.
In a large bowl, mix the butter and vanilla until smooth and no lumps remain. Add the sugar and mix together until smooth and thoroughly combined.
Add the flour and corn starch. Mix with a sturdy spatula or wooden spoon until all flour is incorporated. It may seem like too much flour at first, but just keep mixing until it’s all incorporated.
Dump mixture out onto a generously-floured work surface and knead for about 30 seconds until dough forms into a ball and is not sticky. Divide dough in half and set one portion aside.
Lightly flour your rolling pin and roll out the dough until it's ¼-inch thick (see Café Tips above in post.) Add more flour to work surface and rolling pin as needed if dough is sticky.
Cut into your favorite shape and place on prepared sheet pans. Knead dough scraps together, roll and cut out shapes until dough is used up.
Place pan in refrigerator, uncovered, for at least one hour and up to 12 hours.
When ready to bake, preheat oven to 350˚F. Remove cookies from refrigerator.
Bake for 8 minutes. Remove pan from oven and sprinkle lightly with sugar. Flatten any puffed part of cookies with the back of a flat metal spatula. Sprinkle cookies with more granulated sugar. Return to the oven for 5-7 additional minutes, or until light golden brown.
Allow to cool on pan for 5 minutes then transfer to a cooling rack to cool completely. Store in an airtight container. Hide the container if you plan to serve these to guests.