Preheat your oven to 350°F (175°C). Line a 9x9 or 8x8 inch baking pan with parchment paper, or spry with cooking spray.
Mix flour, sugar, and a teaspoon of salt in a medium bowl. Cut in the butter with a fork, pantry cutter, or your fingers. Continue cutting in the butter until the mixture resembles coarse crumbs. Gently mix the sourdough and discard until it begins to come together. It will look like a pie dough.
Press evenly into the bottom of the prepared pan. Bake for 15-20 minutes until lightly golden. Remove and cool slightly.
Prepare the Lemon Mixture. In a medium saucepan, whisk together sugar, cornstarch, and 1/4 teaspoon of salt. Stir in the water, lemon juice, and lemon zest. Cook over medium-high heat, stirring frequently, until the mixture boils. Once the mixture reaches a boil, reduce the heat to low and let it simmer for 1 minute. The mixture should thicken considerably.
In a small bowl, whisk egg yolks and eggs. Gradually whisk in about 1/2 cup of the hot sugar mixture to temper the egg yolks. This step prevents the eggs from cooking.
Pour the tempered egg yolks back into the saucepan. Bring the mixture to a gentle boil and continue cooking, stirring constantly, for 2 minutes. The filling should be thick and smooth.
Remove from heat. Add 2 tablespoons of butter and stir until fully incorporated.
Assemble. Pour the filling over the crust, spreading out to smooth if necessary.
Bake: Bake for 20-25 minutes or until the filling is set. Cool to room temperature, then chill for at least 2 hours.
Finish. Dust with powdered sugar, cut into bars, and serve chilled.