Heat the oven to 350°F. In the bowl of a mixer, beat together the butter, sugars, lemon zest, and salt until light and fluffy. Add the egg, vanilla, and baking powder; beat until well combined. Reduce the mixer speed to low, and add the flour, beating until a dough forms. Wrap and refrigerate dough 1 hour or freeze for up to 2 months.
Place the dough on a well-floured clean surface, and roll out to a scant ¼-inch thickness. Cut out three 5-inch circles, and place them in 4-inch tart or mini pie pans. Repeat with the remaining dough to make six tarts.
Fill the tarts with pastry weights, and place on a baking sheet. Bake in the oven, removing the pie weights after 12 minutes. Continue baking until lightly golden, about 8 minutes more. Transfer the tarts in their pans to a wire rack, and let cool completely.