Preheat your oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, leaving an overhang on the sides.
In a large bowl, beat the softened butter and powdered sugar together until creamy and smooth. Add the flour and salt, then mix on low speed until a soft dough forms and no dry streaks remain. Press the dough evenly into the bottom of the prepared pan.
Bake the crust for 18 to 20 minutes, until the edges are just starting to turn lightly golden. Remove from the oven but keep the oven on.
While the crust bakes, whisk together the eggs, granulated sugar, and flour in a large bowl until smooth. Add the fresh lemon juice and lemon zest, then whisk until everything is fully combined.
Pour the lemon filling over the hot crust immediately after it comes out of the oven. Return the pan to the oven right away.
Bake for 20 to 25 minutes, until the filling is set around the edges and no longer jiggly in the center. It may puff slightly, which is normal.
Let the bars cool completely in the pan at room temperature, then refrigerate for at least 2 hours until fully chilled and firm. Dust generously with powdered sugar, then lift out using the parchment and cut into bars.