Preheat oven to 350 degrees F (180 C). Prepare baking sheets with parchment or silicone mats, if desired, and set aside.
Using an electric mixer, or mixing by hand with a rubber spatula, cream together the butter, brown sugar, and white sugar until well-blended. Beat in the instant pudding mix, followed by eggs and vanilla. Scrape down the sides of the bowl and beat until mixture is mostly even.
Sprinkle the flour, baking soda, and salt over the dough, then mix just until they are incorporated. Stir in chocolate chips by hand.
Drop spoonfuls of dough onto baking sheets and bake for 10-12 minutes, until the tops are lightly golden. Allow cookies to cool for 5-10 minutes on the baking sheets, then remove to a wire rack to cool completely.
Cookies will keep well in an airtight container at room temperature for at least 3-4 days.
Notes
These cookies freeze extremely well as dough balls for future baking. Just shape into balls, place on a baking sheet with a little space in between them, and pop into the freezer for about 30 minutes. That will flash freeze the dough balls, after which you can pile them together in a freezer-safe bag or container without them sticking together. Bake straight from the freezer as needed. Just add 1-2 minutes to the baking time!