Preheat the oven to 350°F (175°C). Grease a 9×13-inch baking dish or line it with parchment paper.

In a large bowl, whisk together the all-purpose flour, baking powder, and salt until evenly combined.

In another bowl, beat the eggs and granulated sugar until lighter in color and slightly fluffy. Add vegetable oil, milk, and vanilla extract, and mix until smooth.

Gradually add the dry ingredients to the wet ingredients. Stir gently until smooth and no dry streaks remain.

Pour the batter into the prepared baking dish and spread it evenly. Bake for 22 to 25 minutes, or until a toothpick inserted comes out clean. Allow to cool completely.

In a mixing bowl, beat the cream cheese until smooth. Add the powdered sugar and vanilla extract, and mix until creamy. Fold in the whipped topping gently.

In another bowl, combine the drained crushed pineapple with sugar (if using). Stir to blend.

After the cake has cooled, carefully slice a thin layer from the top. Keep the thicker base in the dish, reserving the thin slice for the middle layer.

Spread a layer of cream filling over the thick sponge base. Spoon the pineapple mixture over the cream and spread gently.

Place the thin sponge layer over the pineapple layer and press lightly. Spread remaining cream filling over the top sponge layer and smooth it out.

Scatter pineapple chunks over the cream layer and sprinkle shredded coconut if using. Cover and refrigerate for at least 2 hours.