Line 2 baking sheets with parchment paper. Whisk the flour, baking powder and salt in a medium bowl. Beat the butter and sugar in a large bowl with a mixer on medium-high speed until light and fluffy, 3 to 5 minutes. Beat in the egg, then the vanilla and lemon zest. Reduce the mixer speed to low; add the flour mixture and beat until just combined (the dough will be soft).
Divide the dough into 4 pieces and put 2 pieces on each prepared baking sheet. Shape each piece into a 12-by-1-inch log, about 3 inches apart. Using the handle of a wooden spoon or your finger, press a 1/2-inch-deep indentation down the middle of each log. Refrigerate until firm, about 30 minutes.
Position racks in the upper and lower thirds of the oven and preheat to 375 degrees F. Fill the indentations with jam. Bake, switching the position of the pans halfway through, until golden brown, 20 to 25 minutes. Let cool completely on the baking sheets, then transfer the logs to a cutting board and slice crosswise into 1-inch-wide cookies.