Preheat oven to 350 degrees F. Line an 8 x 8 inch square pan with parchment paper. Place two overlapping strips going in either direction with some parchment hanging over both sides of the pan.
In a medium sized mixing bowl, stir the lime zest into the flour. Stir in the baking powder, powdered sugar, and cornstarch. Add the cubed butter. Toss the butter to coat. Use a pastry cutter, fork or your hands to work the butter in until it resembles coarse meal.
Use your fingertips or the bottom of a 1 cup measuring cup to press the mixture firmly and evenly into the pan.
Bake for 11-15 minutes, until edges are very lightly golden.
Lime Filling
While the crust bakes, prepare the filling. In a medium sized mixing bowl, whisk together sugar, eggs, lime zest, lemon juice and lime juice. Whisk in the flour. Avoid overmixing.
When the crust has finished baking, give the filling mixture a final stir then pour it over the crust. Immediately return the pan to the oven and bake another 28-30 minutes, or until the filling is set. The bars are ready when the edges are set and the filling is a little wiggly but not liquid. They'll continue to set as they cool then chill.
Set pan on a wire rack. Allow bars to cool completely at room temperature for about 1 hour then place the whole pan in the refrigerator to chill for another 1-2 more hours so that bars are somewhat chilled when serving.
When ready to serve, lift the bars out of the pan. Dust some powdered sugar and zest a little fresh lime on top. Use a long sharp knife to cut bars into 9, 12, or 16 squares and enjoy!
Notes
Juice: I highly recommend fresh lime or lemon juice. Freshly squeezed juice has much better flavor. Air bubbles: Do not overmix the filling and add the eggs and lemon juice at the same time. This will prevent lots of air bubbles from forming on top. It's normal for air bubbles or even a white layer of air bubbles to form on top of your baked bars. These are from the air from the eggs rising to the surface. The bars will still taste the same. You can cover the bubbles up by dusting powdered sugar over them before serving!Cool and chill: I let the bars cool at room temperature for about 1 hour. After that, I set the pan in the refrigerator for 1-2 more hours til they're somewhat chilled. Cutting: Use a long sharp knife. Wipe knife clean between each cut. Storage: Store bars in an airtight container in the refrigerator for up to 4 days. Store in a single layer. You can also freeze them for up to two months.