I've been experimenting with different flours and butter.
Bread flour, almost any brand, will give you a cookie with a thick shell. I also like the results of cookies made with White Lily all-purpose. White Lily weighs a little less cup for cup, so the best way to use it is to weigh out the 13.5 oz. If you don't have a scale, stir it well and use about 3 1/3 cup instead of 3 cups. Cookies made with White Lily won't have as thick a shell and will be slightly softer.
For the butter, I've used European style (Central Market brand or Plugra) and have also experimented with regular unsalted butter. The best cookies were with the European style butter, but unsalted Land o Lakes also gave me big, fat cookies. When I used store brand (HEB) butter, the cookies spread a little bit more.