Heat oven to 350°F (175°C). Whisk egg yolks and sugar until thick, about 2 minutes, then whisk in flour, salt, milk, lemon juice, lemon zest, melted butter, and vanilla until smooth.

In a separate bowl, beat egg whites on medium until foamy, then on high until stiff, glossy peaks form, about 3 minutes total.

Stir a third of the whites into the lemon base, then gently fold in the rest until only a few small streaks remain.

Pour batter into an ungreased 1½-quart baking dish. Place in a water bath and bake for 45 to 55 minutes, until top is golden and springy and the pudding layer jiggles slightly.

Rest the cake for 10 minutes, then scoop warm portions that catch both the sponge and the lemon sauce.