Mix self-rising flour, butter, sugar, eggs, vanilla extract, and salt thoroughly in a bowl; beat at least 5 minutes. Refrigerate dough at least 2 hours to overnight.
Preheat oven to 275 degrees F (135 degrees C).
Roll dough out on a floured work surface using a lightly floured rolling pin; cut cookies out with cutters.
Place cookies onto baking sheets.
Bake in the preheated oven until cookie bottoms are lightly golden brown, about 15 minutes.