In a separate bowl, whisk together the flour and salt.
2 cups all purpose flour, ¼ teaspoon salt
Gradually add the flour mixture to the butter mixture, mixing on low speed until the dough comes together.
Transfer the dough to a lightly floured surface and knead gently just until the dough comes together.
Roll the dough into a 1/4-inch-thick sheet and cut into desired shapes using a cookie cutter. (I used 3-inch diameter round cookie cutters and this made 2 dozen cookies.)
Place the cookies on a baking sheet lined with parchment paper.
Bake for 10-12 minutes, or until the edges are lightly golden brown.
Remove the cookies from the oven and let them cool for a 3-4 minutes on the baking sheet.
Transfer the cookies to a wire rack to cool completely.
In a medium bowl, whisk together the powdered sugar, milk and 1-2 drops of purple food coloring.
Drizzle the glaze over the cooled cookies and (optional) top with more dried lavender.
Dried culinary lavender buds
Notes
Butter: If you're using salted butter, omit the salt.
Flour: It's important to properly measure the flour to avoid dry or heavy cookies. Weighing the flour is the most accurate method. Otherwise, stir or sift the flour to break it up. Then lightly spoon it into the measuring cup and level.
Lavender: It's important to use culinary lavender in this recipe.
Milk: Any milk from skim milk to whole milk will work. Nondairy milk, like almond milk, will also work but may alter the color of your icing.