Whisk the flour, baking soda and salt together in a bowl and set aside.
In the bowl of a stand mixer with the paddle attached, beat the butter and both sugars just until creamy and well blended.
Add each egg one at a time, beating on medium speed just until blended. Beat in the vanilla paste (or vanilla). Scrape side of bowl often.
With mixer on lowest speed, gradually add the flour mixture, stopping often to scrape side of the bowl. This is a very thick, slightly dry dough so you may want to use your hands to mix or even empty onto a pastry mat and push it all together. Before it is completely mixed, mix in the chocolate chips.
Divide the dough into 24 pieces. Wrap each section tightly around an Oreo. Chill the dough balls for at least 30 minutes or until ready to bake.
Preheat oven to 375 degrees F. If your oven runs hot you can use 350F, but 375 gets the job done quicker and the cookies are a little brownie.
Grease 12 muffin tin cavities (or 24 if you are baking them all at once).
Bake until golden brown and set, about 15 minutes. Let cool in the muffin tins for 5 minutes, then loosen but don't remove. Let cool completely at room temperature of in the freezer.
If baking without the muffin tins, follow the same directions as above, but preheat to 375F and bake at 375F for about 10-12 minutes (or longer if you want them very brown).