Preheat oven to 350°F and line a baking sheet with parchment paper.
In a large bowl, cream together butter, brown sugar, and granulated sugar until smooth and fluffy.
Add eggs and vanilla extract, mixing until fully combined.
In a separate bowl, whisk together flour, cocoa powder, cornstarch, baking soda, and salt.
Gradually mix dry ingredients into wet ingredients until just combined.
Fold in chocolate chips.
Chill dough for 30 minutes.
Scoop large dough balls (about ¼ cup each) and place on baking sheet. Slightly flatten tops.
Bake for 9–11 minutes until edges are set and centers are slightly underbaked.
Cool on baking sheet for 10 minutes, then transfer to a wire rack.
In a bowl, beat peanut butter, butter, and powdered sugar until smooth.
Add vanilla, salt, and heavy cream until thick and spreadable.
Melt chocolate chips and coconut oil in microwave in 30-second intervals, stirring until smooth.
Spread or pipe peanut butter frosting onto cooled cookies.
Drizzle melted chocolate over the top and let set before serving.