Preheat oven to 350 degrees and line a 9×13-inch pan with parchment paper.: You will notice the warm air circulating as the oven approaches temperature, which helps the crust bake evenly. Properly lining the pan prevents sticking and makes lifting the whole slab out simple. If the parchment slips, use a dab of butter at the corners to secure it. Common mistake to avoid, do not skip lining or the crust can adhere to the pan and tear when removed.
To make crust, combine the flour, powdered sugar and salt in a food processor. Add butter pieces. Pulse until mixture resembles fine crumbs. Press into bottom of parchment lined baking dish.: After pulsing you should see pea sized pieces of butter distributed through the pale flour mixture, and the aroma will turn slightly rich and nutty as the butter breaks down. Press firmly and evenly into the pan so the crust bakes to a uniform thickness. If you press unevenly, some areas will brown faster than others. A failing to chill the dough briefly can cause shrinking while baking.
Bake for 18 to 20 minutes.: As the crust bakes you will see the edges begin to take on a light golden hue and a faint, toasty butter scent will fill the kitchen. This visual cue means the base is set and will support the filling. Underbaked crust will be soggy once the filling is added, while overbaked crust can become too hard. Keep an eye in the last few minutes to avoid darkening.
Make the filling while the crust is baking. Using a food processor or blender, process the lemon juice, lemon zest, and strawberries until smooth.: The blender will create a vivid pink mixture that smells simultaneously citrusy and floral. Processing thoroughly gives a uniform texture that bakes into a glossy custard. If the mixture seems watery, pulse briefly and let it settle so you can check the consistency. One trap is blending too long and heating the fruit, which can alter the fresh flavor.
In a medium bowl, whisk together granulated sugar, powdered sugar, flour and salt. Add eggs and egg yolk and whisk well.: Whisking these dry ingredients with the eggs creates a cohesive base that helps the filling thicken as it bakes. You should feel the mixture smooth out and take on a slightly thicker body. Take care not to over whisk to the point of frothing, because excess air can cause the filling to puff and crack. A common error is adding cold eggs which can cause uneven mixing, so use room temperature eggs if possible.
Add the strawberry mixture and whisk to blend.: Once combined, the batter will be uniformly pink and will glisten when moved. The scent will be a bright blend of tangy lemon and sweet strawberry . Incorporating the fruit puree ensures a consistent flavor in every bite and prevents pockets of unmixed liquid. Avoid vigorous whisking that traps air, as that can change the custard texture.
As soon as you take the crust out of the oven, pour the filling on top and return to the oven for another 18 to 20 minutes or until set in the middle.: Pouring while the crust is hot helps the filling adhere and bake evenly. During the second bake watch for the center to appear just set with a slight jiggle when nudged, and the edges should look firmer than the middle. The aroma will amplify with a warm fruity perfume. Overbaking will dry the filling and create cracks, underbaking will leave it runny after chilling, so aim for a slight wobble in the center.
Cool bars to room temperature and then refrigerate for at least 2 to 3 hours before serving.: Cooling lets the filling finish setting and chilling firms the bars for clean slicing. You will notice the filling lose its glossy sheen as it cools and turn into a custardy texture. Rushing this step is a frequent mistake that results in sloppy slices, so allow the chill time for best results.
Cut into squares and dust with powdered sugar.: The final step brings visual charm and a soft sweetness on the surface. Use a sharp knife warmed briefly under hot water and wiped dry to get neat edges. Press the powdered sugar through a fine sieve for an even dusting. Cutting too soon can cause crumbling; wait until fully chilled for tidy squares.