Preheat your oven to 350°F (175°C).
Line a baking sheet with parchment paper.
Cream together the softened butter and packed brown sugar until light and fluffy.
Beat in the egg and vanilla extract until well combined.
Stir in the crushed pineapple until evenly distributed.
In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture, stirring until just combined.
Drop rounded balls of dough onto the prepared baking sheet, leaving space between each cookie.
Bake for 12-15 minutes, or until the edges are lightly golden.
Let the cookies cool on the baking sheet for a few minutes before transferring to a cooling rack.
Mix together the confectioners' sugar, lemon zest, and a few tablespoons of water or milk to prepare the frosting.
Once cooled, generously frost each cookie with the lemon frosting.