Preheat the oven to 300 degrees Fahrenheit.
Butter two 9-inch cake tins and line the bottoms with parchment paper, and then butter the parchment paper as well. This will make it much easier to get the shortbread out of the pan.
In the bowl of a stand mixer, or in a large bowl, beat together the sugar, butter and vanilla until fluffy.
Add all of the flour at once and, using the paddle attachment on your stand mixer at medium-high speed, or with a fork, mix together just until the dough comes together.
Gather any crumbly bits into a ball of dough, then divide the dough into two. Using your fingers, gently press in each ball of dough into the prepared cake pan. The parchment can make this a little difficult because it tends to slide, but be patient. Once the dough is in the pan, you can smooth it out by laying a sheet of parchment temporarily on top and smoothing with your fingers. Once the dough has been smoothed, press holes into the dough using the tines of a fork in a decorative pattern. Repeat for the other ball of dough in the other cake tin.
Place both cake tins in the oven and bake for 35 minutes until the top is lightly golden and the edges are a deeper gold.
Remove the tins from the oven and immediately turn the cookie out on a chopping board. Do this in a swift motion so the cookie doesn't break -- remember, it's still quite soft at this stage.
Use a pizza wheel or knife to cut the cookie into wedges. You can cut each circle into 8 really large cookies, or 12 smaller ones.
Transfer the cookies to a rack and cool thoroughly before eating.