Blend flour, sugar and salt in a food processor for 5 seconds. Add butter pieces and process, using the pulse button until mixture resembles coarse meal. Add yolks and vanilla and blend until dough holds together. Press dough onto the bottom of the buttered (bottom only) springform pan. Brush with the beaten egg. Bake cake until golden and tester inserted into center comes out clean, about 55 minutes. Serve warm or at room temperature.