In a large bowl, whisk together the eggs, lemon juice, baking powder, remaining 1/4 cup flour, and 2 cups of sugar.
Pour the lemon custard mixture on top of the cooled basil lemon shortbread. Gently tap the pan on the counter a few times to release any air bubbles.
Bake in the 350-degree oven for 30-35 minutes, until the lemon curd is set. Let the Basil Lemon Bars cool on a wire rack for about 1 hour.
Then, cut into 2-inch squares and dust with powdered sugar.
You can keep the Basil Lemon Bars covered in the fridge for 3-4 days.