Begin by making the shortbread dough for your Lavender Lemon Sandwich Cookies. In a food processor, combine powdered sugar, unsalted butter, egg yolk, salt, culinary lavender, and all-purpose flour. Pulse until the mixture is just combined.
Next, shape the dough into disks to chill. Divide the mixture into two equal parts, flattening each into a disk about 1 inch thick and refrigerate for about 20 minutes.
Once chilled, roll out one disk of dough between two sheets of parchment paper until it's about ¼ inch thick. Use a round cookie cutter to cut out circles.
Freeze the cutouts for at least 20 minutes before baking. This will help them maintain their shape while baking.
With the cookies frozen, place them in the preheated oven and bake for about 11 minutes.
While the cookies cool, prepare the buttercream frosting by whisking together the egg whites and granulated sugar, then beat until medium peaks form before adding the unsalted butter.
Assemble your cookies by piping the buttercream onto the bottom of one cookie and topping with another cookie.