**Preheat the Oven:** Preheat your oven to 350°F (175°C). Line the baking pan with parchment paper, leaving overhang for easy removal.
**Make the Crust and Crumble:** In a large bowl, combine flour, granulated sugar, brown sugar, baking powder, and salt. Cut in the cold butter using a pastry cutter or fork until the mixture resembles coarse crumbs. Stir in the beaten egg until just combined.
**Assemble the Crust:** Press half of the mixture firmly into the bottom of the prepared pan to form an even layer. Reserve the other half for the crumble topping.
**Prepare the Lemon Filling:** In a medium bowl, whisk together eggs, sugar, flour, lemon juice, and zest until smooth and well combined.
**Pour and Top:** Pour the lemon filling over the crust. Sprinkle the reserved crumble mixture evenly over the top.
**Bake:** Bake for 35-40 minutes, or until the topping is golden and the lemon filling is set. Let the bars cool completely in the pan.
**Chill and Slice:** Refrigerate for at least 2 hours before slicing into squares or bars for clean cuts.