Preheat your oven to 350°F (175°C). In a mixing bowl, combine the all-purpose flour, powdered sugar, and softened butter. Use a pastry cutter or your fingers to mix until the texture is crumbly. Pack this mixture into a greased 8x8-inch baking dish, pressing firmly to create an even layer. Bake in the oven for 15 minutes, or until the crust is lightly golden.

While the crust is baking, combine the granulated sugar, cornstarch, and water in a medium saucepan. Cook this mixture over medium heat, stirring constantly until it thickens and begins to bubble. In a separate bowl, temper the beaten egg yolks by mixing in a small amount of the hot filling, then stir this back into the saucepan along with the fresh lemon juice and zest. Cook for an additional 2 minutes until the filling is glossy.

Once the lemon filling is prepared, carefully pour it over the hot crust in your baking dish. Return it to the oven and bake for another 10 minutes, allowing the filling to set properly.

While the filling is baking, start on the meringue. In a large mixing bowl, beat the room-temperature egg whites with cream of tartar using an electric mixer. Continue beating until soft peaks form, which usually takes about 2-3 minutes. Gradually add in granulated sugar, continuing to beat until stiff peaks form and the meringue is glossy and smooth.

Remove the lemon filling from the oven and immediately spread the meringue over the hot lemon layer. Use the back of a spoon to create peaks for a beautiful texture. Return to the oven and bake for another 10 to 15 minutes until the meringue is golden and has a slight crispness.

Let the lemon meringue pie bars cool completely in the baking dish. For clean slicing, it's best to chill them in the refrigerator for at least 1 hour. Once well chilled, use a sharp, dry knife to slice the bars into squares or rectangles.