1. Make the dough. Cut butter into ¼-inch pieces. Let stand 10 minutes to soften.
2. In the bowl of a stand mixer fitted with paddle attachment, add butter and sugar. Beat on high speed until pale and fluffy, about 2 minutes, scraping down sides of bowl as needed.
3. With mixer on low, add egg and vanilla; increase mixer speed to medium-high and beat until egg is well incorporated.
4. Sift together flour, salt, and cornstarch. With mixer on low, slowly add flour mixture to bowl. When crumbly, increase speed to high, beat 1 minute.
5. Transfer dough to the middle of a piece of parchment cut to the size of sheet pan. Place a second sheet of the same sized parchment over the dough; slightly flatten dough. Using a rolling pin, roll dough to ¼-inch thick.
6. Transfer parchment with dough to a sheet pan. Refrigerate 2 hours.
7. Make the cookies. Preheat oven to 375° F.
8. Remove sheet pan from refrigerator; remove top parchment paper. Transfer bottom parchment with dough to flat surface. 
9. Cut desired shapes from dough. Remove excess; set aside. Add new parchment to same sheet pan. Place cookie shapes on parchment-lined sheet pan, 1-inch apart.
10. Place pan in oven. Bake 9-12 minutes, or until cookies are lightly browned on bottom. 
11. Remove pan from oven. Immediately transfer cookies to cooling rack.

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