Preheat your oven to 350℉ (180℃). Prepare a 9x9 inch baking pan by lining the bottom and two adjacent sides with parchment paper. Lightly grease the remaining sides and set the pan aside. Melt the butter and let it cool for approximately 15 minutes.
In a separate mixing bowl, combine the flour, baking powder, baking soda, salt, and cornstarch, whisking until evenly mixed.
In a large bowl, whisk together the cooled melted butter, oil, brown sugar, and white sugar until fully combined. Add the eggs and vanilla extract to the sugar mixture and whisk vigorously for 2–3 minutes, until light and slightly aerated.
Gently fold the dry mixture into the wet using a spatula, taking care not to fully incorporate the flour—leave some streaks. Stir in the shredded coconut until the batter becomes uniform with no visible dry patches.
Spread the batter evenly into the prepared pan. Optionally, sprinkle 1–2 teaspoons of white sugar across the surface for a light crust. Bake for 28–35 minutes, or until a toothpick inserted into the center comes out clean—32 minutes is often ideal.
Once baked, the edges should appear lightly golden with a soft center. Allow the bars to cool completely in the pan before slicing and serving.