Preheat your oven to 350°F (175°C).
In a bowl, whisk together the flour, baking soda, and salt.
In another bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.
Add the egg and vanilla extract to the butter mixture, mixing until fully combined.
Gradually add the dry ingredients to the wet mixture, mixing just until combined.
Fold in the caramelized pineapple and chopped cherries gently.
Scoop tablespoon-sized portions of dough onto a baking sheet lined with parchment paper.
Bake for 10-12 minutes, or until the edges are golden and the centers are set.
Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.