In a medium bowl, combine the flour, lavender, baking powder, and salt. Set aside.
In the bowl of a stand mixer using the paddle attachment or in a large bowl using a hand mixer, cream together the butter and sugar. Add the egg and vanilla, beating until smooth. With the mixer on low speed, add the flour mixture, stirring until just combined.
Turn the dough out onto a lightly floured surface and divide it in half. Shape each half into a log, about 1 3/4 inches in diameter and 8 inches long. Wrap the logs in plastic wrap and refrigerate for at least 1 hour. (You can refrigerate the logs as long as overnight, or freeze them for up to several months. Thaw, if necessary, before proceeding.) For the cookies in the photo, I squared off the log, for square-ish cookies.
Preheat the oven to 375°F. Line baking sheets with parchment.
Cut the logs into 3/8-inch slices. Arrange the slices on the prepared baking sheets, about 1/2-inch apart. Bake until just beginning to turn golden at the edges, 11 to 13 minutes. Place the baking sheets to a cooling rack and cool thoroughly before decorating with royal icing (recipe below), if you like. (For the cookies in the photo, I also sprinkled on some silver decorating dust.)
For the royal icing:
In the bowl of a stand mixer using the whisk attachment, a large bowl using a hand mixer, or a medium bowl using a whisk, combine the sugar, egg white, and lemon juice on slow speed, mixing until thick and smooth.
Color the icing as desired. Use a pastry bag or a resealable bag with a corner snipped off to drizzle the icing over the cookies.
Notes
A note on lavender
Dried lavender flowers are available at specialty food stores and in the bulk dried herbs and flowers section at many natural food stores. Besides using them in this recipe, you can sprinkle them into other baked goods or try rubbing them under the skin of poultry before roasting.
About the Royal Icing
This icing is purposefully thin enough to drizzle. If you want stiffer icing, use 1 1/2 to 2 cups of sugar. If you're concerned about using raw egg whites, substitute with the equivalent amount of dried egg whites and water.
A note on the provided nutrition information
The nutrition information provided has been estimated by an online nutrition calculator and is not a substitute for a professional nutritionist’s advice.