Preheat oven to 350 degrees F. I always use an oven thermometer. Ovens can, and usually do, heat at a different temperature than what shows on your oven screen. For the best results in any of your baking, I highly recommend using an oven thermometer. Line your baking sheets with parchment paper.
In the bowl of a stand mixer with the paddle attachment, add your cool unsalted butter, sugar, and salt. The temperature of the butter and the fact that you use unsalted butter matter here.
Turn your mixer on the lowest speed available. We don't want to incorporate any air into the dough. Air will cause spreading! We only want to mix this until it starts to incorporate.
Add the 2 cold eggs and the vanilla. Again, the temperature of the eggs matter. You want to use them cold.
Again, turn your mixer on to the lowest speed and mix just until the eggs and vanilla have incorporated into the butter and sugar. It will still look sort of lumpy or curdled. This is ok. You just don't want any big chunks of butter. Scrape down the bottom and sides of your bowl. If you need to, mix for a few more seconds.
Add the flour to your butter, sugar, egg mixture. Mix for a few seconds to 1 minute and then add in your crushed Oreos.
Once more, turn your mixer on to the lowest setting, and mix until it all comes together. It will start to clean the sides of the bowl and gather onto the paddle. It doesn't take long, so don't walk away from it. Turn the mixer off and touch the dough. If you can leave an imprint with your finger without the dough sticking to it, its ready. I live in a humid area, but the amount of flour in the recipe is perfect 9 1/2 times out of 10.
I use a piece of parchment paper very lightly sprinkled with flour to roll my dough. I also use two pieces of 3/8 inch thick wood as my guide to roll my dough between. This will give you perfectly even cookies every time!
Take half of your dough, place it onto the very lightly floured parchment paper, and very lightly sprinkle some flour over the dough.
Using a rolling pin, roll your dough out and cut into the shapes you need.
Place your cut dough onto your parchment paper covered cookies sheets and bake in your preheated oven for 10-14 minutes depending on the size of your cookies. I never have to bake over 14 minutes, even for my largest cutter (5 1/2 inches). You don't want your cookies to brown.
After removing from the oven, let the cookies set on the cookie sheet for 2-4 minutes.
Move them onto a cooling rack to cool completely.
I usually let my cookies sit in a tupperware container on a paper towel overnight before decorating. This will help grab any extra butter so you don't get that dreaded "butter bleed" after you've spent 2 days decorating them!
Enjoy your delicious, thick, soft (but sturdy), sugar cookies! Feel free to let your imagination run wild with the flavor possibilities!