Preheat your oven to 350°F (175°C). Line an 8x8-inch baking pan with parchment paper, leaving an overhang on the sides.
In a medium bowl, mix flour, sugar, and fine sea salt for the crust.
Add olive oil and stir until the mixture forms a soft dough.
Press dough evenly into the bottom of the prepared pan.
Bake crust for 18-20 minutes, or until lightly golden.
Meanwhile, prepare the filling: In a medium bowl, whisk together sugar and flour.
Add eggs, lemon zest, and lemon juice; whisk until smooth.
Pour the lemon mixture over the hot crust as soon as it comes out of the oven.
Return to the oven and bake for 18-20 minutes more, or until the filling is set and no longer jiggly.
Cool completely at room temperature, then refrigerate for at least 2 hours.
Once chilled, lift the bars out of the pan using the parchment overhang.
Sprinkle lightly with flaky sea salt and powdered sugar if using.
Cut into squares and serve.