Preheat your oven to 350°F (175°C). Line an 8x8 inch baking dish with parchment paper, leaving some overhang on the sides for easy removal later.
In a medium bowl, whisk together 1 cup of flour, 1/4 cup of powdered sugar, and 1/4 teaspoon of salt. Add in the chilled and cubed butter and use your fingers or a pastry cutter to mix until the mixture resembles coarse crumbs.
Press the mixture evenly into the bottom of the prepared baking dish, making sure to press down firmly. Bake for 20 minutes.
In the meantime, prepare the filling. In a medium bowl, whisk together the eggs and granulated sugar until well combined. Add in the lemon juice, lemon zest, and 1/4 cup of flour. Whisk until smooth.
Pour the filling over the hot crust and return to the oven. Bake for an additional 20-25 minutes, until the filling is set and lightly golden brown.
Allow the bars to cool completely before removing them from the baking dish using the parchment paper overhang. Dust with powdered sugar before slicing and serving.
These Lemon Bars can be stored in an airtight container in the refrigerator for up to 3 days.