Preheat oven to 375°F and line a cookie sheet with parchment paper.
In a large bowl, whisk together melted butter and sugars.
Whisk in egg and vanilla extract.
Whisk in peanut butter.
Fold in the flour, baking soda and salt until just combined.
Add the chocolate chips and fold until just combined.
Scoop 1/4 cup cookies, flattening each one to around 1 inch (2.5 cm) thick with your hands or a fork. Transfer the cookies to the prepared baking sheet, leaving 2 inches (5cm) between each cookie.
Bake cookies for 8-10 minutes, until the cookies are barely golden brown and don't look wet on top. Cool on the baking sheet or on a wire rack.