In a large bowl, combine 3/4 cup unsalted softened butter along with 3/4 cup granulated sugar, and 1 tsp vanilla extract. Mix everything together using an electric hand mixer. Beat on high speed until the butter is light and pale.
Now sift in 1 1/2 cups of flour along with 1/4 tsp salt. Use the hand mixer to combine everything together again.
Once the cookie dough is well mixed, transfer it to a large piece of plastic wrap. Then shape the dough into an 8-inch log. Then wrap it tightly and place it into the freezer for about 30 minutes. It may take more or less time depending on how cold your freezer is.
Once the shortbread log firms up, unwrap it and roll it onto a plateful of course sugar. I used about 1/4 cup of course sugar. Add more if needed.
Once the exterior of the cookie log is coated, slice the cookies unit 1/4 inch slices.
Place the cookies onto a baking sheet lined with parchment paper and bake in a preheated 350 degree Fº oven for about 10 minutes.
Notes
Beat the butter well- Because there is no leavening agent in this recipe, beating the butter will incorporate air bubbles. So mix it until the butter is light and pale.
Wrap the dough in plastic wrap before rolling- Getting sticky dough into a log shape is difficult, so wrap it in plastic wrap and use that to shape it. So much easier!
Roll the dough in sugar before cutting- It will take a lot longer if you try to roll individual cookies in the coarse sugar. Instead, do it as a log, then slice the cookies off and bake.
Make ahead: You can prepare the dough for these cookies ahead of time and then wrap the log in plastic wrap and refrigerate. You can then roll it in sugar, slice it, and bake the cookies when you're ready.