In the bowl of a stand mixer fitted with the paddle attachment, cream together the confectioner's sugar and butter until light and fluffy. With the mixer running on low, slowly add in the flour, a little at a time and continue mixing until everything is well-combined. Add in the vanilla and mix until well-distributed. Feel free to add a tablespoon or two of almond milk at this point to make the dough come together if it's still a bit crumbly.

Add in the culinary lavender and mix until it's well-distributed throughout the dough.

Roll the dough out to 1/8" thickness and cut out cookies with cookie cutters. Continue re-rolling and cutting out cookies from the dough until all the dough has been used up.

Bake cookies on a silpat-lined baking sheet at 325° for 12 minutes, rotating the baking sheet halfway through.

Allow the cookie to cool completely on a wire rack. Meanwhile, make the glaze by combining the second amounts of confectioner's sugar and vanilla, along with the almond milk in a small dish. Mix until smooth and drizzle over cooled cookies.