Whisk egg, vanilla, and 1 tablespoon of water in small bowl and set aside.
Place flour, sugar, baking powder, salt, and lemon zest in food processor and pulse to combine. Scatter butter pieces over flour mixture and process to cut butter into flour until mixture resembles coarse meal, about seven 1-second pulses. With machine running, add egg mixture and process until all liquid ingredients are incorporated. Squeeze handful of dough; if it forms moist ball, no more water is necessary. If mixture is crumbly and dry, add 1 more tablespoon water and process until just incorporated.
Remove dough from food processor and transfer to large bowl. Gently knead until cohesive, about 30 seconds. Shape dough into 5-inch disk. Wrap in plastic wrap and refrigerate for at least 2 hours or up to 2 days.
Remove dough from refrigerator (if refrigerated longer than 1 hour, let stand at room temperature until malleable). Roll dough between 2 large sheets of lightly floured parchment paper to 13-inch circle about 1⁄4 inch thick. Peel off top sheet, loosely roll dough around rolling pin, then unroll over 10-inch tart pan with removable bottom. Working around circumference of pan, ease dough into pan corners by gently lifting edge of dough with one hand while pressing into corners with other hand. Press dough against fluted sides of pan, patching breaks or cracks if necessary. If some sections of edge are too thin, reinforce by folding excess dough back on itself. Run rolling pin over top of tart pan to remove any excess dough. The finished edge should be 1⁄4 inch thick. If not, press dough up over edge of pan and pinch. Freeze dough-lined pan for 30 minutes.