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