In mixing bowl, add your cool unsalted butter, sugar, and salt. The butter should still be cool, not cold but not room temperature as well, otherwise this will cause the cookies to spread. Unsalted and salted butter have very different water percentage contents. Using salted butter can and often will cause spreading.
Turn mixer to lowest speed available so as to not incorporate any air into the dough. Air will also cause spreading! Mix together mixture just until incorporated.
Mix in the 2 cold eggs and the vanilla to the mixture and beat at lowest speed just until the eggs and vanilla are just incorporated in. Make sure the eggs are cold, another reason the cookies will hold shape. The mixture will be lumpy looking. Just make sure their are no big chunks of butter and mix more if you need to if needed, while scraping down sides and bottom of bowl as needed.
Add the flour and turn your mixer on to the lowest setting, and mix until it all comes together. It will not take long for it all to come together. 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.
Remove dough and roll into a ball. Split the dough in half to start rolling dough. Place other half aside. Prepare a work surface with a light dusting of flour on surface, hands and rolling pin.
Using floured hands, flatten out the dough a bit, then use a rolling pin to roll it and smooth it out to be THICK, about ⅜ inch. Use a measuring tape to make sure.
Lightly dust your chosen cookie cutters with flour. Press firmly into the dough, utilizing your space wisely.
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. Don't bake over 14 minutes. You want these to be thick and soft and once they are cooled, they will be just that!
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.