Preheat oven to 350°F and line baking sheets with parchment paper.
In a large bowl, cream together butter, brown sugar, and granulated sugar until light and fluffy. Mix in egg and vanilla.
In another bowl, mix together flour, cornstarch, baking soda, and salt. Mix dry ingredients into wet ingredients until combined. Stir in about 3/4 of the Reese's Pieces.
Scoop dough by the teaspoon and roll each into a small ball before placing on parchment. Slightly flatten each ball and place extra Reese's Pieces on top.
Bake for 7-9 minutes, and let rest on baking sheet for 1-2 minutes before removing to a rack to cool completely.