Preheat your oven to 350°F (175°C). Line your 9x9 inch baking pan with parchment paper, allowing some overhang on the sides for easy removal later.
In a large mixing bowl, combine the melted butter, 1 cup of granulated sugar, 1 cup of all-purpose flour, baking soda, baking powder, and salt. Mix until well combined. Press this dough evenly into the bottom of the prepared baking pan.
Place the pan in the preheated oven and bake for 10-12 minutes, or until the edges are lightly golden. Remove from the oven and allow it to cool slightly while you prepare the filling.
In another mixing bowl, beat the softened cream cheese with an electric mixer until smooth and creamy. Add in 1/2 cup of granulated sugar, 2 tablespoons of all-purpose flour, the egg, and vanilla extract. Mix until everything is well incorporated and smooth.
Fold in the sweetened shredded coconut into the cheesecake filling, ensuring it is evenly distributed.
Pour the coconut cheesecake filling over the slightly cooled crust in the baking pan. Use a spatula to spread it evenly.
Return the pan to the oven and bake for an additional 25-30 minutes, or until the center is set and the edges are lightly golden. The filling will continue to firm up as it cools.
Once baked, remove the pan from the oven and let it cool on a wire rack. After it has cooled to room temperature, refrigerate for at least 2 hours before slicing into bars.