Preheat oven to 350 degrees.
In a large bowl or base of stand mixer, beat together butter, sugar, and brown sugar until light and fluffy, about 3 minutes.
Beat in eggs and vanilla until well combined.
In a small bowl, stir together flour, cornstarch, baking soda, and salt. Gradually beat mixture into butter mixture, scraping down sides as needed.
Stir in chocolate chips.
On an ungreased baking sheet, spread about 1/2 tbsp of dough to a 2 inch round circle. Place about 1 teaspoon of peanut butter in middle of circle. Take another 1/2 tbsp of dough and spread into another 2 inch round circle. Place circle on top of peanut butter and press down edges. Repeat and leave about 2 inches between each cookie.
Bake for 12-14 minutes, or until tops begin to brown.