Preheat the oven to 350 degrees.
Mix flour and baking soda in large mixing bowl, set aside.
Cream butter and white sugar until creamy. Slowly add brown sugar. Add pudding powder. Mix.
Add vanilla; mix. Add eggs; mix until creamy. Slowly add flour/baking soda mixture until stiff.
Add chocolate chips. Mix by hand. Using a cookie scoop, place a scoop of dough onto a greased cookie sheet.
Gently press an Oreo cookie onto the dough, flattening the scoop.
Add another scoop of dough on top of the Oreo.
Use your fingers to crimp the dough together around the Oreo until it is completely encased. Repeat for remaining cookies.
Bake at 350 degrees for 12-14 minutes or until lightly browned and cracking on top. Cool; remove from cookie sheet.