In a large bowl, beat together the butter, peanut butter and sugars until light and fluffy. Stir in the eggs and vanilla until fully combined.
In a separate bowl, whisk together the flour, baking soda, cornstarch and salt. Slowly add the dry ingredients to the wet ingredients, and mix until fully combined. Stir in the chocolate chips.
Refrigerate for 30 minutes.
Preheat the oven to 350˚F.
Drop rounded tablespoonfuls of dough onto ungreased cookie sheets. Bake for 8-10 minutes, or until the edges begin to turn golden brown. Let cool on wire racks.