Preheat oven to 350 degrees F. Line a 8x8 square pan with two sheets of parchment paper, making sure the parchment extends over the sides of the pan to form a "sling". Secure the sides with binder clips if you would like.
In a food processor, pulse together the flour, sugar, salt and lavender until well blended. You want the lavender to be dispersed and chopped up a bit.
1 ¼ cups all purpose-flour, ¼ cup granulated sugar, ¼ teaspoon fine sea salt, ½ teaspoon culinary lavender
Add in the cubes of butter and pulse until the mixture is sandy and starts to form clumps.
½ cup unsalted butter, cut into cubes, cold
Gently press shortbread mixture into an even layer over the bottom of the prepared pan. Refrigerate for a minimum 30 minutes.
Bake crust for 25-30 minutes or until the crust starts to turn a golden brown.
Remove shortbread from the oven, let it cool slightly and reduce the temperature to 325 degrees F.
For the lemon filling:
In a medium bowl, blend together the sugar and lemon zest with your fingers to release the oils from the zest. The mixture should be damp and very fragrant.
1 ⅓ cup granulated sugar, 1 tablespoon lemon zest
Whisk in the flour and salt until blended.
3 tablespoon all purpose flour, pinch of fine sea salt
Add the eggs and whisk briskly so that the sugar doesn't "cook" the eggs and form clumps.
4 large eggs
Add the lemon juice and cream and whisk to fully incorporate.
⅔ cup lemon juice, freshly squeezed, ⅓ cup heavy cream
Pour the filling over the warm shortbread and bake for an additional 25-30 minutes, until filling looks set and doesn't jiggle.
Let the bars cool to room temperature, about 1 hour. Place in the refrigerator to cool for an additional hour. The longer they cool, the easier and prettier they are to slice.
Transfer bars to a cutting board and cut into squares or wedges. Using a sieve, sprinkle with confectioner's sugar and serve.