Heat the oven to 325°F. Coat an 8-inch square baking pan (about 2 inches tall) with cooking spray. Line the bottom and sides of the pan with 2 sheets of parchment paper, positioning them perpendicular to each other and making sure they are long enough to hang over all four sides by at least 1 inch to form a sling.

Beat 4 large egg whites in a stand mixer with the whisk attachment, starting at low and gradually increasing to high speed, until stiff peaks form, about 2 minutes. Transfer to a medium bowl.

Add 4 large egg yolks, ¾ cup granulated sugar, 1 tablespoon finely grated lemon zest, 2 tablespoons of the lemon juice, and ¼ teaspoon kosher salt to the stand mixer (no need to clean). Beat with the whisk attachment on medium speed until the sugar is dissolved, very light in texture, and pale yellow, 5 to 6 minutes. Do not undermix. Scrape down the bottom and sides of the bowl.

With the mixer on medium speed, drizzle in 1 stick melted and cooled unsalted butter until well-incorporated. Scrape down the bottom and sides of the bowl.

Switch the whisk attachment to the paddle attachment. Sift ¾ cup all-purpose flour over the egg yolk mixture. Beat on low speed until no dry spots remain, scraping down the bottom and side of the bowl as needed. Beat in 1 ¾ cups whole milk, ¾ teaspoon lemon extract, and the remaining 2 tablespoons lemon juice until combined.

Add the whipped egg whites to the batter. Gently stir together by hand with a whisk or flexible spatula about a dozen times. The batter will be very thin with a distinct lumps of whipped egg whites at the top of the batter. Do not overmix.

Transfer the cake batter to the baking pan and smooth the top. Bake until the edges are set, the top is golden-brown, and the center wobbles when the pan is jiggled, about 35 minutes for a metal baking pan or 40 to 45 minutes for a glass or ceramic baking dish. Do not overbake.

Let cool completely, about 2 hours. Cover loosely with plastic wrap and refrigerate for at least 1 hour or up to 12 hours. Grasping the excess parchment, remove the cake from the pan and place on a cutting board. Dust lightly with powdered sugar and cut into 9 or 12 pieces.