01 - Preheat the oven to 350°F. Line two baking sheets with parchment paper.
02 - In a small saucepan, melt 4 tablespoons butter over medium heat. Add brown sugar and stir until dissolved and bubbling, about 2 minutes. Remove from heat.
03 - Spoon about 1 teaspoon of the caramel mixture onto each spot where a cookie will bake, spacing 2 inches apart. Top each with a few pieces of pineapple and half a cherry.
04 - In a medium bowl, whisk together flour, baking soda, cream of tartar, and salt.
05 - In a large bowl, beat softened butter with granulated sugar until light and fluffy, about 2 minutes. Beat in the egg and vanilla.
06 - Gradually add the dry ingredients to the wet mixture, mixing just until combined.
07 - Using a 2-tablespoon cookie scoop, portion dough and roll into balls. Flatten slightly, then place each dough disc atop a prepared pineapple-cherry spot, pressing gently.
08 - Bake for 13 to 15 minutes, or until edges are just golden.
09 - Cool on the pan for 5 minutes, then carefully invert each cookie onto a wire rack so the pineapple topping is on top. Allow to cool completely before serving.