Preheat the Oven: Preheat the oven to 350°F (175°C). Line a 9×13-inch baking pan with parchment paper for easy removal.
Prepare the Shortbread Base: In a medium bowl, combine flour, butter, and sugar. Use a pastry blender or fork to mix until the mixture resembles coarse crumbs. Press the mixture into the prepared pan, forming an even base.
Bake the Base: Place the shortbread base in the oven and bake for 10-15 minutes or until the edges are lightly golden.
Prepare the Pineapple Coconut Topping: While the base is baking, mix melted butter, sugar, and egg in a medium bowl until smooth. Stir in the drained pineapple and shredded coconut.
Assemble the Bars: Once the shortbread base is baked, pour the pineapple coconut mixture over it and spread it evenly.
Bake the Squares: Return the pan to the oven and bake for 30-35 minutes, or until the topping is golden brown.
Cool and Slice: Let the bars cool in the pan for about 20-30 minutes. Once cooled, refrigerate for 20-30 minutes to make slicing easier. Cut into squares and serve.