Cut butter into 1/2-in. cubes and freeze in a single layer until very cold, 10 to 20 minutes. In a food processor, whirl flour and salt until blended.
Add butter and pulse on and off just until butter is about the size of peas. In a small bowl, lightly beat egg and yolk with 3 tbsp. ice water.
Add egg mixture, about half at a time, and pulse just until evenly moistened and holding together (you may need to add 1 more tbsp. ice water as you're pulsing).
Flatten the dough into 2 rough squares, each about 6 in. across. Wrap disks in wax paper. Chill until cold, at least 1 hour and up to 3 days.
Preheat oven to 35
Remove dough from refrigerator and let stand 5 minutes. Unwrap and, on a lightly floured surface, roll dough halves into 1/8-in.-thick squares, 10 to 11 in. each.
Transfer each square to a rimmed baking sheet and prick all over with a fork.
Bake until medium brown, 25 to 35 minutes. Cool on pan, about 30 minutes. Thinly spread baked canap dough with tapenade. Top with goat cheese, pressing it slightly into the tapenade so it sticks, and sprinkle with 1 tbsp. fresh thyme leaves.
