Preheat your oven to 350ºF (180ºC) Line two large cookie sheets with parchment paper.
In a medium-sized bowl, whisk together the flour, cornstarch, baking powder and salt until well blended.
In a large bowl, beat the butter and lavender sugar with an electric mixer on medium speed, until pale and fluffy. Add the the egg white and the vanilla extract 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 cookie dough. Fold it in gently, but don't over mix it. You want to see swirls of blueberry.
Place 2-tablespoon size portions of dough about 2 inches apart onto the prepared cookie sheets. I used a #30 portion scoop.*** Sprinkle with decorative sugar if desired.
Bake until the tops of the cookies are set and the bottom edges turn light golden brown, about 10-14 minutes. Transfer the cookies to a cooling rack. Do not over bake your cookies or they will become dry & crumbly. Test one cookie before baking the entire batch if you are unsure about how to determine the doneness of cookies.