Preheat oven to 350 degrees F. Line 2 baking sheets with silicone liners or parchment paper. Set aside.

In the bowl of a stand mixer, cream together the butter, brown sugar and white sugar until creamy and smooth, about 1 minute. Gradually add in the eggs, one at a time, followed by the vanilla. Lastly, add in the baking soda, salt, flour, and dry pudding mix until a soft dough comes together. Add in the chocolate chips.

Using a Tablespoon-size cookie dough scoop, scoop out a ball of cookie dough and gently flatten it in your palm. Place the Oreo on top of the cookie dough. Scoop out another ball of dough and press it on top. Use your hands to conform the cookie dough around the Oreo so no Oreo is seen. Place 2-3" apart on the baking sheets.

Bake for 12-15 minutes, rotating pans halfway through baking time until cookies are golden brown and set. Cookies may appear slightly underdone; this is okay and you should not over bake! They'll continue to finish cooking on the baking sheet. Cool for about 15 minutes before serving.