Preheat the oven to 350°F. Line an 8×8-inch metal baking pan with parchment paper, leaving an overhang on the sides to help lift the bars out later.

In the bowl of a stand mixer fitted with the paddle attachment, beat the softened butter for about 20–30 seconds until smooth. Add the granulated sugar and mix for 1–2 minutes until fully combined and slightly lighter in color, but not fluffy. Mix in the vanilla extract, lemon zest, and kosher salt. Add the sourdough discard and mix until fully incorporated.

In a separate bowl whisk together the flour and cornstarch. Add the dry ingredients to the mixer and mix on low speed just until the dough comes together and no dry streaks remain. Do not overmix.

Press the dough evenly into the prepared pan. If the dough feels sticky, you can use the saved butter wrapper or the bottom of a measuring cup to help smooth it into an even layer.

Bake for 18–22 minutes, or until the edges are lightly golden and the center is set. Allow the crust to cool slightly while preparing the lemon filling and reduce the oven temperature to 325°F.

Place the cold cubed butter in a bowl and set a fine mesh strainer over the top. In a medium saucepan combine the sugar and lemon zest. Rub the zest into the sugar with your fingers for about 30 seconds to release the lemon oils.

Whisk in the cornstarch, then add the eggs and egg yolks and whisk until smooth without whipping excess air into the mixture. Whisk in the lemon juice until fully combined.

Place the saucepan over medium-low heat. Switch to a silicone spatula and cook while stirring constantly, scraping the bottom and sides of the pan to prevent the eggs from scrambling. Cook until the curd thickens and reaches about 160°F on an instant-read thermometer, which usually takes about 8–12 minutes.

Immediately remove the pan from the heat and pour the curd through the prepared strainer over the cold butter. Let it sit for about 30 seconds, then gently stir until the butter is melted and the curd is smooth and glossy.

Pour the warm lemon curd over the baked crust and gently tap the pan on the counter to release any air bubbles. Return the pan to the oven and bake at 325°F for 12–16 minutes, until the edges are set and the center jiggles like firm gelatin when gently shaken. The center may still look slightly loose, but it will finish setting as the bars cool.

Allow the bars to cool at room temperature for about 1 hour, then transfer them to the refrigerator and chill for at least 4 hours, preferably overnight. Once fully chilled, lift the bars out of the pan using the parchment paper and cut into 9 thick bakery-style bars or 12–16 smaller bars. Dust with powdered sugar just before serving if desired. These bars are best served chilled.