Cream butter and sugar in a mixer with paddle. Slowly add egg yolks, beaten egg half, and vanilla. Add flour and mix until just combined. Wrap in plastic wrap and chill at least 2 hours. Remove from refrigerator, unwrap and roll on a floured surface into a 3/8-inch thick circle. Drape into an 11 or 12-inch tart pan and press into corners. Line pastry with parchment paper and fill with dried beans or pie weights and bake at 350 degrees for 20 minutes until light brown. While still warm, remove weights and parchment paper and brush slightly with a beaten egg white, taking care not to use too much and to only brush the inside of the shell. Let tart shell rest at room temperature until ready to fill.
Recipe courtesy of Josh Moulton