Sift together the flour and salt into a medium sized bowl. Put aside.
In the bowl of a stand mixer with the paddle attachment, mix the 1 cup of sugar and 3 sticks of softened butter on low-medium speed, until just combined. Reduce the speed and add the vanilla extract.
Slowly add the flour mixture in increments, and mix until the dough just starts to come together. It will be clumpy and stick to the paddle attachment.
Dump the dough onto a lightly floured board and shape into a rough ball. Try not to 'work' the dough. Using a butter knife, split the dough ball in half.
Shape each into a rough disk and wrap in plastic wrap. Refrigerate for 30 minutes.
Preheat your oven to 350F. Grease & flour ether a shortbread cake mold or shortbread pan, and reserve. I often use a baking spray with flour when making these cookies.
Taking one disk, place on a well floured board. Using a floured rolling pin, roll to the general size of your mold or pan, about 1/2 inch thick. If using a shortbread mold, transfer to the mold and roll into all the nooks and crannies with a sturdy drinking glass. If using a regular pan, press to fit.
Fork prick several times and place into your hot oven to bake.
For a shortbread cookie mold or pan, bake about 20 minutes or until lightly browned on the edges.
For cut/shaped cookies, I only found about 10 minutes will do.
Once baked, allow to cool to room temperature in the pan.
Once cooled, prepare your chocolate and peppermint candy: Break apart the white chocolate into a microwave safe, small to medium sized bowl, and do the same for the semisweet chocolate into a separate bowl.
Starting with the semi-sweet chocolate, heat for 30 seconds and remove from the microwave. Stir the melted and unmelted portions together until you get a smooth and glossy chocolate. (This takes about 1 minute in a 1300W microwave. Since the chocolate 'keeps its form' for a while when microwave heated, make sure to try and stir it every 30 seconds. Don't overmelt the chocolate or the texture will change.)
Add the peppermint extract to the semisweet dark chocolate (1/4 tsp extract per 4 oz. of chocolate) and stir to incorporate
Pour on to the shortbread still in the pan and smooth with a small offset spatula. Place the whole pan into the freezer for 10 minutes.
Next, take your candy canes or peppermint candies and crush them (I use an old coffee grinder) into small to powdery pieces. Set aside.
Once the semi-sweet chocolate has set, repeat the melting process with the white chocolate in the microwave. Carefully spread on-top of the semi-sweet layer and sprinkle the peppermint pieces on top. Return to the freezer to set for 10-12 minutes, or until hardened.
After chilling, carefully cut around the edge of the pan with a sharp knife, making sure not to cut all the way through - you are just loosening the chocolate.
Slowly invert the pan to a wooden board. Cut into desired size pieces.
Store in a wax paper lined container in a cool & dry place.