In a small bowl, whisk together the flour, cornstarch, and salt ensuring there are no lumps. Set aside.
In a mixing bowl of an electric mixer, mix sugar and lime zest until it looks like wet sand. Then beat softened butter and lime juice until well combined.
Add flour mixture and beat on low speed until thoroughly combined.
The dough will be a bit sticky. Divide the dough in half.
Place a sheet of plastic wrap on your work surface. Place half of the dough on the wrap and cover with a second sheet. Using the plastic wrap to keep the dough from sticking to your hands, form the dough into a round disk. Keeping the dough between the sheets of plastic wrap, use a rolling pin, and roll the dough to just under1/2" thick.
Bring the edges of the plastic up to wrap the rolled-out dough. Repeat with the other half of the dough.
Place rolled-out dough onto a flat sheet and refrigerate or freeze until firm. This will take about 30-60 minutes.
Once the dough is firm, preheat the oven to 350 degrees F.
Remove the top layer of plastic wrap, reserving it for subsequent rollings. Dip cookie cutters into flour before each cut then cut desired shapes out of rolled-out dough. Place cut-out cookies onto an ungreased baking sheet. Brush off any excess flour.
Bring together scraps and reroll between plastic wrap and cut shapes, repeating until finished. Remove the other half of the dough from the refrigerator and repeat the cutting process until finished. (I like to bake the first tray while I'm working on the second.)
Bake cookies for 8-10 minutes or until set. Cool for 5 minutes on a cookie sheet, then remove to a cooling rack to finish cooling.
