Cookie Dough Oreos

package (15.25 ounces) Super Moist Triple Chocolate Fudge Cake Mix (Betty Crocker makes this) OR another similar chocolate cake mix

package (3.9 ounces) instant chocolate pudding mix (dry, do not prepare)

large eggs

shortening (can substitute 1/2 cup butter)

unsalted butter (at room temperature, not melted at all)

brown sugar (lightly packed)

heaping 1/4 teaspoon salt

and 1/2 teaspoon vanilla extract

white flour

miniature chocolate chips

milk (1% or higher fat content)