1. Make the curd: Bring passion-fruit puree, lemon juice, sugar, salt, and cornstarch to a simmer in a medium saucepan over medium heat. Slowly whisk in egg yolks. Cook, whisking constantly, until thick enough to coat the back of a spoon. Remove from heat. Add butter; whisk until melted. Pour through a fine sieve into a medium bowl. Place plastic wrap directly on surface of curd. Refrigerate until set, about 2 hours.

2. Make the cookies: Whisk flour, baking powder, and salt in a medium bowl. Put butter and granulated sugar into the bowl of an electric mixer fitted with the paddle attachment. Mix on medium-high speed until pale and fluffy, about 2 minutes. Mix in the egg and vanilla. Reduce speed to low. Gradually mix in flour mixture. Stir in coconut. Shape dough into 2 disks; wrap each in plastic. Refrigerate until cold, about 30 minutes.

3. Preheat oven to 375 degrees. Turn out 1 disc of dough onto a lightly floured work surface; roll to a scant 1/4 inch thick. Using a 1 1/4-inch cookie cutter, cut rounds of dough; place on parchment-lined baking sheets. Repeat with remaining dough. Freeze until firm, about 15 minutes.

4. Bake until edges of cookies just turn golden, 8 to 10 minutes. Let cool completely on sheets on wire racks.

5. Transfer curd to a pastry bag fitted with a medium round tip (such as Ateco No. 12). Pipe curd onto flat side of a cookie; sandwich with another cookie. Repeat with remaining curd and cookies. Dust with confectioners' sugar before serving.