In the bowl of an electric mixer fitted with the whisk attachment, cream butter and 1/3 cup sugar until fluffy. Add lime zest, juice and vanilla; beat until fluffy. In a medium bowl, whisk together flour, cornstarch and salt. Add to butter mixture and beat on low speed until combined.
Between two 8x12-inch pieces of parchment paper (or waxed paper), roll dough into two 1-1/4-inch-diameter logs. Chill at least 1 hour.
Heat oven to 350. Place remaining 2/3 cup sugar in a resealable plastic bag. Remove parchment from logs; slice dough into 1/8-inch-thick rounds. Place rounds on baking sheets, spaced 1 inch apart.
Bake cookies until barely golden, about 15 minutes. Transfer cookies to a wire rack to cool slightly, 8 to 10 minutes. While still warm, place cookies in the sugar-filled bag; toss to coat. Bake or freeze remaining dough. Store baked cookies in an airtight container for up to 2 weeks.
Points: 62 total; 1 each for 42+ cookies
The dough for these cookies can be frozen in logs for up to two months.