Preheat oven to 350 F. (175 C.) Pour ½ cup sugar and 2 tsp. dry culinary lavender into a food processor. Pulse on a purée setting until lavender is very chopped into the sugar. About 30 seconds.
Pour lavender sugar and 1 cup white granulated sugar into a mixing bowl. Mix until fully incorporated.
In a separate mixing bowl, add 4 oz. melted butter, ¼ cup mixed lavender sugar and 1 tsp. vanilla extract. Once combined, add 1 cup flour and mix into a smooth, crumbly dough. Refrigerate for 10-15 minutes.
Cut a circle of wax paper and place it in the tart tin. You only want it to go halfway up the sides. This is optional. I just find it makes removing the tart much easier later.
Press dough evenly into the tart tin, working it up the sides and all around the interior. If the dough is still a little sticky, simply lay a sheet of cellophane over it while you press it into shape.
To prevent the tart dough from rising while it bakes, line the uncooked tart dough with foil or wax paper. Then, add pie weights on top. Bake for 25-30 minutes. If you use wax paper for your weight, it will be done closer to 25 minutes. If you use foil, it will be done closer to 30 minutes.
While dough bakes, add zest from 1 lemon, ½ cup fresh lemon juice and 4 eggs to the remaining lavender sugar. Whisk together. Then, gently whisk in ¼ cup flour until thoroughly combined. It will seem very liquidy for a custard base. Don’t worry, it’s supposed to.
Once crust is ready, carefully remove tin from the oven and remove the weight. Place tin on a baking sheet for easy placement back into the oven. Carefully pour liquid custard into the crust, then very carefully place tart back into the oven.
Reduce temperature to 325 F. (160 C.) and bake for 30 minutes. Once done, remove from oven and allow it to cool for 10-20 minutes. Cover with cellophane, chill for 4 hours and serve.