In a large mixing bowl, use your electric mixer to beat sugar and butter for 3-4 minutes. You'll want it to have an airy, soft texture. Add in vanilla extract and combine well with mixer.
Add in your flour, 1/2 cup at a time. Your dough should now have a crumbly texture. Use a spatula, wooden spoon or hands to form a ball and then flatten into a disk. Wrap disk in plastic wrap and refrigerate for at least one hour. Let cookie dough thaw out at room temperature for 30 minutes before trying to roll out with a rolling pin.
Add flour to the surface that you're going to roll the dough out on. Add a bit of flour onto rolling pin as well. Roll dough out until it is just slightly over half a centimeter thick.
If possible, use a 2 inch wide, circular cookie cutter. Place cookies onto baking sheet that has been lined with parchment paper. These cookies will not spread so it's fine to place them close together. Sprinkle a bit of turbinado sugar onto each cookie before placing them in the oven. Place sheet on the bottom rack.
Bake for 12 minutes at 350°F. Bake one sheet at a time. I was able to fit 24 cookies on each sheet. You can bake them for a few more minutes if you'd like them to be more golden and crispy. After removing sheet from the oven, allow cookies to cool on sheet for about 5 minutes before transferring them to a wire rack to finish cooling.