Yield: 24 bars.
2 cups + 3 tablespoons all-purpose flour
½ cup powdered sugar
½ teaspoon fine salt, divided
3 tablespoons cornstarch
2 sticks (8 ounces) cold unsalted butter, cut into small pieces, plus more for coating the baking dish
3 teaspoons dried lavender buds
1¾ cups granulated sugar
4 large eggs
4 large egg yolks
1 cup freshly squeezed lemon juice (from 5 medium lemons)
1 tablespoon finely grated lemon zest (from 1 medium lemon)
Powdered sugar, for dusting
Preheat oven to 350°. Coat a 13 x 9-inch baking dish with butter; set aside.
Place 2 cups of flour, powdered sugar, cornstarch, and ¼ teaspoon of salt in the bowl of a food processor fitted with a blade attachment. Pulse briefly to combine. Gradually add the butter pieces over the flour mixture and pulse until the dough just begins to come together, about 20 pulses. Add the lavender and pulse 5 times.
Crumble the dough into the prepared baking dish, pressing firmly and evenly into the pan. Bake on the middle oven rack, until the crust is fully set and just starting to brown on the edges, about 20 to 25 minutes. Remove from the oven and let cool. Reduce oven temperature to 325°.
For the filling: Combine the remaining 3 tablespoons flour, the remaining ¼ teaspoon salt, granulated sugar, eggs, and egg yolks in a large bowl, and whisk until the sugar has dissolved and the mixture is smooth, about 2 minutes. Add the lemon juice and zest, and whisk until well combined.
Pour the filling over the baked crust, return to the oven, and bake until set, about 25 to 35 minutes. Remove from the oven and let cool on a wire rack. Cut into squares and dust with powdered sugar.