Start by browning your unsalted butter. In a saucepan over medium heat, melt the butter while stirring constantly until golden brown. Let it cool slightly.
In a large mixing bowl, combine the browned butter, light brown sugar, and granulated sugar. Blend until smooth and creamy.
Add in the large egg and vanilla extract, mixing until fully incorporated.
In another bowl, whisk together the all-purpose flour, cornstarch, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Gently fold in the semi-sweet chocolate chips and peanut butter chips.
Cover the dough and chill it in the refrigerator for at least 30 minutes.
Preheat your oven to 350°F (175°C) during the last few minutes of chilling.
Using a cookie scoop or tablespoon, drop rounded balls of dough onto a baking sheet lined with parchment paper. Bake for 10-12 minutes.
Remove the cookies from the oven and let them cool on the baking sheet for about 5 minutes before transferring to a cooling rack.