Preheat oven to 350 degrees. Cream butter and sugar in bowl of electric mixer fitted with paddle attachment until light and fluffy. Beat in vanilla and yolks one at a time, beating well after each addition. Add flour and salt; beat just until combined. Do not overmix.
Transfer batter to 9-inch tart pan with removable bottom; with small offset spatula, spread batter and smooth top. (If necessary, chill batter 10 minutes before smoothing.) Place pan in refrigerator 15 minutes.
Remove from refrigerator. Brush top with beaten egg, and mark a criss-cross pattern with a fork. Brush again with egg. Bake until cake is deep golden brown and edges pull away from sides of pan, about 50 minutes.
Transfer to a wire rack to cool slightly. Remove cake from pan, and slice while still warm. Serve with strawberry compote.