Preheat your oven to 350°F (175°C) and line your baking sheets with parchment paper.
In a large mixing bowl, combine the softened unsalted butter, creamy peanut butter, light brown sugar, and granulated sugar. Using an electric mixer, beat on medium speed until the mixture is light and fluffy, about 2-3 minutes.
Add the two large eggs, one additional egg yolk, and the vanilla extract to the butter mixture. Beat again until everything is well combined.
In a separate bowl, whisk together the all-purpose flour, instant vanilla pudding mix, baking soda, and salt. Gradually add this dry mixture to the wet ingredients, mixing on low speed until just combined.
Gently fold in the dark chocolate melting wafers or semi-sweet chocolate chips with a spatula until they are evenly distributed throughout the dough.
Using a cookie scoop or tablespoon, drop rounded balls of dough onto the prepared baking sheets, spacing them about 2 inches apart. Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden but the centers are still soft.
Remove the baking sheets from the oven and let the cookies sit for a few minutes before transferring them to a cooling rack.
