Pulse the nuts and 1/4 cup granulated sugar in a food processor until finely ground. Pulse in the flour and baking powder. Beat the butter, brown sugar and 1/2 cup granulated sugar in a large bowl with a mixer on medium-high speed until fluffy, 3 to 5 minutes. Beat in the egg and both extracts. Reduce the mixer speed to medium low; beat in the nut-flour mixture. Divide the dough in half and shape each piece into a disk; wrap each disk in plastic wrap. Refrigerate until firm, at least 2 hours or overnight.
Meanwhile, make the filling: Bring the dried pineapple, passion fruit, remaining 2 tablespoons granulated sugar and the water to a simmer in a saucepan over medium heat. Cook until the pineapple is very soft, 6 to 8 minutes. Pulse in a mini food processor. Let cool.
Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Working with 1 disk at a time, roll out the dough on a floured surface until 1/4 inch thick. Cut out stars using a 3-inch cookie cutter. Arrange 1 inch apart on 2 unlined baking sheets. Reroll the scraps and cut out more cookies. Cut out 1-inch stars from the centers of half the cookies. Refrigerate until firm, 20 minutes.
Bake, switching the pans halfway through, until the cookies are golden, 18 to 20 minutes.
Let cool 5 minutes on the pans, then transfer to racks to cool completely.
Spread the filling on the whole cookies. Dust the cutout cookies with confectioners' sugar and carefully place on top of the filling.
Photograph by Ryan Dausch