Preheat the oven to 350 degrees. Line two baking sheets with parchment paper or silicone baking mats.
In a medium mixing bowl, whisk together the flour, baking soda, and salt.
In the bowl of an electric mixer, beat together the butter and sugars on medium high speed until lighter in color and fluffy, at least 3-4 minutes, scraping the bowl halfway through.
Add the instant pudding mix (just the powder!), eggs, and vanilla extract and beat until well combined, another 2-3 minutes, scraping the bowl as needed.
Stir in flour mixture starting on low speed, then increasing to medium speed until fully combined,.
Add the chocolate chips and Oreos and beat on low speed until well distributed.
Scoop a generous 2 Tablespoons of dough (a rounded jumbo-size cookie scoop) onto the prepared pans, about 2 inches apart.
Bake for 10-12 minutes, or until edges are set but center is still puffed and soft looking. Top with additional Oreo chunks and chocolate chips if desired. Allow to set up on the pan for 5-10 minutes before transferring to a wire rack to cool.