Drain the canned pineapple rings completely. Place them on multiple layers of paper towels, cover with more paper towels, and press gently to extract as much moisture as possible. Let sit for at least 15 minutes.

In a large bowl, cream together the softened butter and granulated sugar until light and fluffy, about 2-3 minutes. Beat in the egg and vanilla extract.

In a separate bowl, whisk together the flour, baking powder, baking soda, and salt. Gradually mix the dry ingredients into the wet ingredients until just combined.

Cover the dough tightly with plastic wrap and chill in the refrigerator for at least 1 hour.

Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.

Scoop about 2 tablespoons of dough per cookie and roll into balls. Place on the baking sheet spaced 3 inches apart. Flatten each ball slightly with your hand.

Press one dried pineapple ring firmly into the center of each flattened cookie. Generously sprinkle the entire cookie and pineapple ring with coarse sugar.

Bake for 14-16 minutes until the edges are deep golden brown. Let cool on the baking sheet for 10 minutes before transferring to a wire rack to cool completely.