Preheat oven to 350°F Line 2-3 cookie sheets with parchment.
Cream butter and vanilla with mixer. In a separate bowl, sift together powdered sugar, cornstarch, flour and salt. Gradually add dry ingredients to butter, beating constantly on high until the batter is the consistency of whipped butter (about 5 minutes).
Drop dough by heaping teaspoons onto prepared cookie sheets. Bake for about 15 minutes, or until cookies begin to turn golden on edges.
Immediately after removing cookies from oven, press one chocolate piece into the center of each cookie. Cool completely.