In a standing mixer or with a hand mixer, cream the butter until smooth.
Add the salt and sugar and cream together until light and fluffy.
Add the vanilla and mix again briefly.
Add half the flour, mix until just coming together, then add the remaining half mixing again until the dough starts to form a cohesive ball.
Empty your bowl onto the counter and using your hands, work it together and form it into a square. Wrap this in plastic and refrigerate for 2 hours or up to 2 days.
Position racks in upper and lower thirds of the oven and preheat to 325℉ (163℃). Prepare 2 pans by lining them with parchment paper.
Unwrap the dough and roll out to roughly a 9 x 9-inch square. Frequently turning the dough helps to maintain the shape as you roll.
Using a large knife, score the dough into squares, or use a cookie cutter.
Dust the tops of the cookies with sugar or leave plain if dipping in chocolate. Bake 13-15 minutes or until a pale gold color has been achieved.
Once the cookies have cooled completely.
Melt the chocolate in the top of a double boiler.
Once the chocolate is completely melted, remove from heat and begin to dip your shortbread.
Dipping one corner in, lower the cookie half way into the chocolate then remove, shaking off the excess before placing on a wire rack to set.
After every three or four cookies, stop to sprinkle salt on the cookies you just dipped.
*Chocolate Shortbread can be made by replacing a quarter of the flour with unsweetened cocoa powder.