Preheat your oven to 350°F (180°C). Prepare an 8-inch square baking pan by lining it with parchment paper or lightly greasing it.

In a mixing bowl, combine all-purpose flour, ½ cup butter, and ¼ cup granulated sugar. Mix until resembling coarse crumbs. Press into the bottom of the pan and bake for 15 minutes.

In another bowl, cream together 1 tablespoon of butter with ½ cup of sugar until light and fluffy. Add the room-temperature egg and mix well. Fold in the well-drained crushed pineapple and half of the shredded coconut.

Spread the topping mixture evenly over the baked shortbread base. Sprinkle the remaining coconut on top. Bake for an additional 25-30 minutes, until set and lightly toasted.

Allow the Coconut Pineapple Squares to cool completely in the pan, then cut into squares to serve.