Preheat oven to 350 F and line a 13x9 baking pan with parchment paper. Be sure that parchment hangs over the edges, you will use it to lift out the bars when they are cool.
Make the Crust
In bowl of your food processor, pulse to combine flour, powdered sugar and butter. Process until coarse crumbs are formed, just as the dough begins to come together. Dump crumb mixture into prepared pan and press evenly. Bake for 18-20 minutes, until lightly browned. Remove from oven and allow to cool on wire rack.
Make the Lemon Filling
With an electric mixer set at medium speed, beat granulated sugar, flour, eggs, lemon juice, and lemon zest until ingredients are well blended.
Pour mixture evenly over warm crust. Return to oven; bake until center is set and edges are golden, about 18-20 minutes. Remove pan to wire rack; cool completely (about 2 hours).
When completely cool, refrigerate for about 30 minutes to help set the filling.
Remove bars from fridge and lift out of pan using parchment paper handles. Sift some powdered sugar across the top and cut into bars (approximately 2" x 1.5", 30 bars).
These lemon bars will cut neatly if you chill them first. Store in the fridge for about 30-40 minutes. Any longer and the shortbread becomes to solid to get through easily. This is from the butter solidifying. If that happens, leave them at room temperature for 20 minutes or so.
Store lemon bars tightly covered at room temperature.
The instructions call for a food processor, simply because it's easier and faster. You can use your mixer for the filling, and if you prefer, you can cut the butter in the old fashioned way, with your fingers or using two butter knives scissor fashion.