Preheat your oven to 175°C (350°F). Line a 9-inch square baking pan with parchment paper, leaving some overhang for easy removal.
In a mixing bowl, combine 1 cup of flour, 1/4 cup of sugar, and a pinch of salt. Use a pastry cutter or your fingers to work in the cold butter until the mixture resembles coarse crumbs and looks like wet sand.
Press this crumbly mixture evenly into the prepared pan, smoothing the top with the back of a spoon or your fingers. Bake for 15 minutes until lightly golden and just set.
Meanwhile, finely zest both lemons using a microplane, avoiding the bitter white pith. Then, juice the lemons to gather about 1/3 cup of fresh lemon juice.
In a separate bowl, whisk together the eggs, 3/4 cup of sugar, 1/4 cup of flour, lemon zest, and lemon juice until the mixture is smooth and slightly frothy.
Pour the lemon custard over the pre-baked crust, spreading it out evenly with a spatula. Return to the oven and bake for an additional 20-25 minutes, until the filling is set around the edges but still slightly wobbly in the center.
Remove from the oven and let the lemon bars cool completely in the pan on a wire rack. Once cooled, refrigerate for at least an hour to set fully.
Dust the cooled bars generously with powdered sugar, then cut into squares. Serve chilled or at room temperature, enjoying the vibrant citrus aroma and smooth, glossy filling.