Preheat oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, leaving overhang for easy removal.
In a large bowl, whisk together 2 1/2 cups flour, powdered sugar, and salt. Pour in melted butter and mix until combined. The mixture will resemble coarse crumbs.
Press the dough evenly into the prepared pan using your fingers or the bottom of a measuring cup. Bake for 20 minutes or until lightly golden brown around the edges.
While the crust bakes, add granulated sugar to a food processor. Zest 3 lemons directly into the sugar and pulse until the zest is fully incorporated and the sugar turns light yellow.
In a large bowl, whisk together the lemon sugar and remaining 1/2 cup flour until well combined.
Add eggs and fresh lemon juice to the sugar mixture. Whisk vigorously until completely smooth and well combined.
Pour the lemon filling over the warm crust. Return to oven and bake for 25 minutes, rotating the pan halfway through, until the center is just set but still slightly jiggly.
Cool completely at room temperature for 1 hour, then refrigerate for at least 2 hours until fully set.
Using the parchment paper overhang, lift the bars from the pan. Dust with powdered sugar and cut into squares using a sharp, clean knife wiped between cuts.
