Whisk the flour, baking powder and salt in a medium bowl. Beat the butter, brown sugar and 1/3 cup granulated sugar in a large bowl with a mixer on medium speed until light and fluffy, about 3 minutes. Beat in the egg, then the lemon juice. Reduce the mixer speed to medium low; mix in the dried pineapple, then the flour mixture until combined. Cover and refrigerate until firm, about 30 minutes.
Meanwhile, combine the crushed pineapple, cream cheese, the remaining 2 teaspoons granulated sugar, the vanilla and lemon zest in a bowl with a rubber spatula, breaking up any large pineapple pieces. Refrigerate until slightly firm, at least 30 minutes.
Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Roll the dough into 1-inch balls; arrange 2 inches apart on the baking sheets. Indent each with the back of a floured 1/4 teaspoon measuring spoon; brush with milk.
Bake, switching the pans halfway through, until the cookies are slightly puffed, 10 to12 minutes. Remove from the oven andre-indent; spoon in the filling. Return to the oven until lightly browned, 6 to 8 more minutes. Let cool 5 minutes on the baking sheets; transfer to racks to cool completely. Top with dried pineapple.
Photograph by Levi Brown
Courtesy of Food Network Magazine