Beat the egg whites and cream of tartar to stiff, glossy peaks. Set aside.

In another bowl, beat the egg yolks and sugar until thick and pale. Mix in the melted butter and vanilla.

Add the flour in two additions, alternating with the milk, mixing just until combined. The batter will be thin and slightly lumpy.

Gently fold the egg whites into the batter in three additions until only a few white streaks remain; the mixture will look curdled.

Pour into an 8-inch square pan lined with parchment. Bake at 325°F (160°C) for 50 to 60 minutes, until the top is golden and the center wobbles like set custard.

Cool completely in the pan on a rack, then refrigerate at least 2 hours until firm. Lift out, slice, and serve.