Preheat the oven to 375°F. In a small mixing bowl, whisk together the flour, cornstarch, baking powder, baking soda, and salt. Set aside. Line two baking sheets with parchment paper and set aside.
Grind the lavender with about ¼ cup of the sugar using a mortar and pestle, spice grinder, or mini food processor until small pieces.
Add the lavender, lemon zest, and remaining sugar to the bowl of stand mixer fitted with the paddle attachment (or a large mixing bowl and a hand mixer). Massage everything together between your fingertips until very fragrant and smells super lemony.
Add the butter and mix on medium speed until light and fluffy, 2 to 3 mintues.
Add the egg, sour cream, and vanilla. Mix again until fully combined.
Stop the mixer and add all of the flour mixture. Mix on low speed to incorporate some of the flour, then mix on medium-low until the dough comes together into a smooth ball.
Roll out about half of the dough at a time until ¼-inch thick. You can lightly dust with flour or roll on a silicone baking mat.
Use a 2 ½ to 3-inch round cookie cutter to cut out the cookies from the dough. Carefully move them to the lined baking sheets, about an inch apart. They do not spread very much.
Bake the cookie for 8 to 9 minutes. When done, they will be light brown on the bottom and set around the edges. Cool on a wire rack.
Repeat with the remaining dough. Decorate as desired!