In a large mixing bowl, blend the melted butter with the creamy peanut butter until you achieve a smooth consistency.
Gradually add the brown sugar and granulated sugar, stirring until the mixture becomes light and creamy.
Incorporate the vanilla extract, egg, baking soda, and salt into the mixture, ensuring everything is well combined.
Slowly add the all-purpose flour, mixing just until the dough starts to come together. Gently fold in the chocolate chips.
Using a spoon, scoop out cookie dough portions roughly 2 tablespoons each. Place the dough balls on baking sheets lined with parchment paper or silicone baking mats. Let the dough chill for about 30 minutes in the refrigerator.
Preheat your oven to 350°F (175°C).
Once chilled, press the dough balls lightly with a fork to create a crisscross pattern on top.
Bake for 8-12 minutes, or until the edges are just beginning to turn golden and the tops have set but still appear slightly soft.
Allow the cookies to cool before transferring them to an airtight container. Store them at room temperature for up to 3 days or freeze for up to one month to enjoy later.