Whisk together the flour, cocoa powder, cornstarch, baking soda, baking powder, salt, and espresso powder in a medium bowl.
In a large mixing bowl, beat the butter, granulated sugar, and brown sugar until light and fluffy, about 2 to 3 minutes.
Beat in the egg, egg yolk, and vanilla extract until smooth and fully incorporated.
Add the dry ingredients and mix on low speed just until combined. Do not overmix.
Fold in the peanut butter chips and chocolate chips until evenly distributed.
Cover the dough and refrigerate for at least 1 hour or up to overnight.
Preheat the oven to 350°F (175°C). Line baking sheets with parchment paper.
Scoop the dough into 2-tablespoon portions and place them about 2 inches apart on the prepared baking sheets.
Bake for 10 to 11 minutes, until the edges are set and the centers still look slightly underbaked.
If desired, press a few extra peanut butter chips and chocolate chips into the tops of the warm cookies.
Let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.