Preheat your oven to 350°F (175°C) and line a 9x9-inch pan with parchment paper, leaving some overhang for easy removal. In a mixing bowl, whisk together all-purpose flour, powdered sugar, and salt. Cut in cold unsalted butter until the mixture resembles coarse crumbs. Press this crumbly mixture evenly into the bottom of the lined pan.

Bake the shortbread crust in the preheated oven for 15-20 minutes, until the edges are lightly golden and the center is set. Remove from the oven and allow to cool slightly while preparing the filling.

In a saucepan, combine granulated sugar, culinary lavender buds, and a cup of water. Warm over medium heat, stirring until the sugar has dissolved. Remove from heat and let steep for 10 minutes, then strain to remove the buds and set aside to cool.

In a mixing bowl, whisk together large eggs and the cooled lavender syrup. Add fresh lemon juice and lemon zest, then sift in powdered sugar and additional flour, whisking until smooth and free of lumps.

Pour the filling over the warm shortbread crust, spreading it evenly. Bake for 20-25 minutes, or until the filling is set but jiggles slightly in the center.

After baking, let the bars cool on a wire rack for about 30 minutes. Refrigerate for at least 2 hours or until fully chilled and firm.

Once chilled, lift the bars out of the pan using the parchment overhang and place on a cutting board. Dust with powdered sugar and garnish with fresh lavender or lemon slices before cutting into squares.