Preheat the oven to 350°F & line a sheet pan with parchment paper. Make lavender sugar by blending the sugar and lavender in a food processor until well combined and fine. Divide out ½ cup into a small bowl and set aside.
In a medium bowl, whisk together the flour, baking powder and salt. In a large bowl, use an electric mixer fitted with a paddle attachment on medium-high speed to beat the butter and remaining 1¼ cups lavender sugar until fully combined. Mix in the egg, egg yolk, and vanilla. Add in the flour mixture. Mix until just combined.
Using a cookie scoop (I used a purple scoop which is about 2 ½ tablespoons), divide the dough into balls, then roll in the small bowl of lavender sugar to coat evenly. Place the dough balls on the parchment lined sheet pans and flatten slightly with your fingers or the bottom of a measuring cup.
Bake for 8-10 minutes (longer for larger cookies), or until the tops of the cookies are set.