Preheat your oven to 350°F (175°C).
In a medium skillet, cook the diced pineapple over medium heat until caramelized, about 8-10 minutes.
In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.
Add the eggs one at a time, mixing well after each addition, then stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking soda, and salt.
Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Fold in the caramelized pineapple and chopped cherries gently.
Drop spoonfuls of dough onto a parchment-lined baking sheet, spacing them about 2 inches apart.
Bake for 12-15 minutes or until the edges are lightly golden.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack.