Line two baking sheets with parchment paper.
Pour the Raw Cane Sugar (1 cup) into a small saucepan. Heat it over medium heat, and stir the sugar until it starts to melt. Turn the heat down to medium-low and continue stirring until it has melted completely.
Pour the melted sugar onto a parchment lined baking sheet and allow it to cool completely, about 15 minutes.
When the sugar has hardened completely, chop into small pieces with a knife and store in the fridge until ready to use.
Zest the Meyer Lemon (2).
Cream the Unsalted Butter (1 cup) and Powdered Confectioners Sugar (1 cup) together on high for 3 minutes, until fluffy and smooth.
Stir in the Ground Lavender (1 tablespoon), Vanilla Extract (1 tablespoon), lemon zest, and Salt (1/4 teaspoon).
Stir in the Cake Flour (2 cup). When it’s coming together but not totally smooth yet, stir in the burnt sugar pieces.
Use your hands to knead the dough until it forms a smooth ball.
Roll half the dough into a log on a large cutting board or clean surface.
Place a piece of plastic wrap at the bottom of the board and roll the log onto the plastic. As it rolls, it will wrap itself in the plastic.
Chill the dough for at least 1 hour.
Preheat the oven to 325 degrees F (160 degrees C).
Unwrap the dough and slice it into 1/2 inch circles. Arrange them on the parchment lined baking sheet and sprinkle with a pinch of the Granulated Sugar (2 tablespoon) - you may not use all of it. Prick the center gently with the tines of a fork.
Bake for 15-20 minutes, or until the cookies are golden brown. Allow to cool completely before eating. You can store the cookies in a sealed container at room temperature for up to 1 week!