An hour before baking (less if your kitchen is warm): take the butter out of the fridge to soften.
In the bowl of a stand mixer, combine the powdered sugar (sifted), butter, sugar and sea salt. With the paddle attachment, beat the mixture for at least 5 minutes, until it’s well combined. Add the egg and vanilla and beat for at least 3 minutes to combine. The mixture will look clumpy.
Place a sieve over the bowl and sift in the flour. Cover the bowl with a tea towel and beat on medium low until the dough comes together. Use your hands and gather the dough into a flat disk. Wrap it in plastic wrap and set in the fridge for an hour or so until the dough is firm but not too stiff to roll out. If you’ve left it for a few hours or overnight, let it soften on the counter until it’s workable
On a lightly floured surface, roll out the dough to about a quarter inch thickness and use a cookie cutter to cut out shapes. Set the shapes on a parchment lined cookie sheet. Don’t crowd them but also don’t worry about leaving too much space, they won’t spread. Set the tray in the freezer and preheat the oven to 350 F.
Bake for 10 minutes until they are just set, don’t wait for the edges or the bottoms to turn golden or they will overbake and be tough.
When the cookies are completely cool, begin tempering the chocolate:
Set the chocolate into three separate heat-proof bowls. Remove about ¼ of the chocolate from each bowl and set aside, this is your ‘seed’.
Microwave the bowls of chocolate for 30 seconds and check them, if none have begun melting then do another 30 seconds. Stir the chocolate and return to the microwave for another 30 seconds. At this point the milk and white chocolate should be somewhat melted but the dark chocolate will still be firm.
As needed, microwave for another 20 seconds. Stop once the chocolate is half melted and stir, stir stir. The heat from the melted chocolate will melt the rest. Add the “seed” you set aside to the bowl and stir again until you have a smooth chocolate. The dark chocolate will take the longest to melt and it’s likely that those ‘seeds’ won’t melt fully (especially if they are large).
Alternate pouring the chocolates into a quarter sheet pan or a pasta bowl (something small-ish and shallow) and gently swirl them with a tip of a butter knife. Dip the cookies face down into the chocolate and hold them upright for a few seconds to let the remaining chocolate slide off. Place on a sheet of parchment paper and allow to set.
Store in an airtight container.