Preheat oven to 350 degrees. Butter a 9-inch tart pan with removable bottom.
Sift both flours, baking powder, and salt into a large bowl; set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat the egg yolks and sugar on medium-high speed until doubled in volume and pale yellow, 2 to 3 minutes, scraping down the sides of the bowl as needed. Add the butter in four parts, beating until completely combined after each, 1 to 2 minutes total. With the mixer on low speed, add flour mixture, beating until combined.
Transfer batter to prepared pan; with a small offset spatula, spread batter and smooth top. (If necessary, chill batter for 10 minutes before smoothing.) Refrigerate for 30 minutes.
Remove pan from refrigerator. Brush top with beaten egg, and mark a crosshatch pattern with a knife. Brush again with egg. Bake until cake is deep golden brown and edges pull away from sides of pan, 40 to 45 minutes. Cover with foil if browning too quickly.
Transfer to a wire rack to cool slightly. Remove cake from pan, and slice while still warm.