In a small bowl, whisk together the cornstarch with 1 tablespoon of water.
In a small saucepan over medium heat, combine the blueberries, lemon juice and remaining 1 tablespoon of water, stirring until the blueberries soften and start to release their juices. Smash the blueberries slightly with the back of the spoon. Stir in cornstarch mixture. Turn the heat down to low. Simmer until thickened to a jam consistency, about 1-2 minutes.
Transfer the blueberry compote to a small bowl and set aside to cool to room temperature.
Lavender Sugar
In a small food processor or a clean spice grinder, combine 1/4 cup of the sugar with the lavender. Pulse a few times to chop the lavender into smaller bits. Add the remaining sugar and pulse a few more times to combine.
Blueberry Lavender Cookies
Preheat your oven to 350ºF (180ºC) Line two large baking sheets with parchment paper.
In a medium bowl, whisk together the flour, cornstarch, baking powder and salt.
In a large bowl, beat the butter and lavender sugar with an electric mixer, until light and fluffy.
Add the the egg white and vanilla and beat until well combined.
On low speed, add the flour mixture in two additions and mix just until combined.
Add dollops of the blueberry compote to the batter. Fold in gently, but don’t completely combine it. You want to see swirls of blueberry.
Place 2-tablespoon size portions of dough about 2 inches apart onto prepared baking sheets. I used a #30 portion scoop.*** Sprinkle with decorative sugar if desired.
Bake until tops of cookies are set and bottom edges turn light golden brown, about 10-14 minutes. Transfer the cookies to a cooling rack. Do not over bake. Test one cookie before baking the entire batch if you are unsure about how to determine the doneness of cookies.