Preheat and Prep: Preheat the oven to 375°F (190°C). Line a 9x9-inch baking pan with parchment paper, leaving an overhang on the sides for easy removal later.
Make the Dough: In a medium bowl, whisk together the 1 ½ cups flour, ½ cup sugar, ½ teaspoon baking powder, and ¼ teaspoon salt.
Cut in Butter: Add the cold butter (1 stick). Using a pastry blender or a fork, cut the butter into the flour mixture until it resembles coarse crumbs (pea-sized pieces).
Add Egg: In a small bowl, lightly beat 1 egg. Pour the beaten egg into the flour mixture and stir until a crumbly dough forms.
Bake the Crust: Press half of the dough mixture firmly into the bottom of the prepared pan. (Reserve the remaining half for the topping). Bake the crust for 10 minutes.
Make the Filling: While the crust bakes, prepare the filling.
In a medium bowl, whisk together the ¾ cup sugar, 3 Tablespoons flour, ½ teaspoon baking powder, and pinch of salt. (Whisking these dry ingredients first prevents flour lumps).
Whisk in the 2 beaten eggs, 6 Tablespoons lemon juice, and lemon zest until the mixture is completely smooth.
Bake the Filling (The "Set" Step): Pour the lemon filling over the hot, pre-baked crust. Return the pan to the oven and bake for 15 to 20 minutes.
Critical Step: Because your filling contains flour and baking powder, it will puff up slightly. Check it at 15 minutes. It must be set and firm to the touch (not liquid) before adding the topping.
Add Topping & Finish: Once the filling is firm, remove the pan from the oven. Crumble the reserved dough evenly over the top. Bake for an additional 15 to 20 minutes, or until the crumb topping is light golden brown.
Cool and Chill: Remove from the oven and cool on a wire rack for 30 minutes. Then, refrigerate for at least 2 hours. Garnish by sprinkling confectioner's sugar over the top (optional) before lifting the parchment paper out of the pan and slicing into squares.