Preheat your oven to 175°C (350°F). In a mixing bowl, combine 1 1/2 cups flour, 1/4 cup powdered sugar, and 1/4 teaspoon salt. Add the cold, cubed butter and use a pastry cutter or your fingers to work it into the flour mixture until it resembles coarse crumbs. Press this mixture evenly into the bottom of your prepared 9-inch square baking pan. Bake for 20 minutes until the edges are just turning golden and the crust looks set.
While the crust is baking, zest both lemons using a zester, then juice them into a bowl, straining out any pulp using a fine-mesh sieve. In a separate bowl, whisk together the eggs, granulated sugar, lemon zest, and 1/4 cup flour until smooth and slightly thickened. Stir in the strained lemon juice until well combined and glossy.
Once the crust has baked and cooled slightly, pour the lemon filling over it, spreading evenly with a spatula. Return the pan to the oven and bake for an additional 20–25 minutes, until the filling is just set around the edges but still slightly jiggly in the center. The top should be glossy and vibrant yellow.
Remove the lemon bars from the oven, let them cool in the pan for about 15 minutes, then transfer to a wire rack. Chill in the refrigerator for at least 2 hours until fully set and cold. This helps the flavors meld and makes slicing easier.
Before serving, dust the top with powdered sugar for a soft, sweet finish. Use a sharp knife warmed slightly to cut clean, neat squares. Serve chilled and enjoy the bright, tangy flavor with a tender, buttery crust.