Preheat the oven to 350ºF (180ºC).
Overturn an 8-inch (20cm) square pan on the counter and wrap the outside snugly with foil, shiny side up. Remove the foil, turn the pan over, and fit the foil into the pan, pressing to nudge the foil into the corners. Smooth the foil as best you can and lightly butter the surface, or spray it with nonstick spray.
In a medium bowl, mix the flour, 1/4 cup (50g) sugar, 1/4 teaspoon salt, 8 tablespoons (115g) melted butter, and vanilla, stirring just until smooth.
Smooth the batter into the bottom of the pan, using your hands to get it as level as possible.
Bake the crust for 25 minutes, or until it’s deep-golden brown.
While the crust is cooking, cut the lemon in half, remove the seeds, and cut the lemon into chunks.
Put the chunks of lemon in a food processor or blender along with the sugar and lemon juice, and let it run until the lemon is completely broken up.
Add the eggs, corn starch, 1/4 teaspoon of salt, and 3 tablespoons (45g) melted butter, and blend until almost smooth. (A few tiny bits of lemon pieces are fine. It doesn't need to be entirely smooth.)
When the crust comes out of the oven, reduce the heat to 300ºF (150ºC). Pour the lemon filling over the hot crust and bake for 25 minutes or just until the filling stops jiggling and is barely set.
Remove from the oven and let cool completely. Once cool, carefully lift out the bars using the overhang of foil as a handle.
Cut the bars into squares or rectangles. Sift powdered sugar over the top just before serving, if desired.
