Preheat oven to 350F. Line two cookie sheets with silpat mats or parchment paper. Cream the butter and sugar together on medium speed until fluffy and light in color in stand mixer.
Mix in egg and vanilla. On low speed, mix in flour, cornstarch, baking soda.
Add in Oreos and mix on low speed until cookies are crushed and thoroughly mixed into dough.
Scoop dough and form balls about 1 1/4 inch in diameter. Make balls smooth and space 2 inches apart. Press gently down on each ball.
Bake for 10-11 minutes, until barely golden brown around the edges.