Preheat the oven to 350°F (175°C). Line a 9-inch round cake pan with parchment paper and set aside.
In a large mixing bowl, combine the softened cream cheese and granulated sugar using an electric mixer or whisk until smooth and slightly fluffy, about 2-3 minutes. The mixture should be creamy with no lumps.
Add the eggs one at a time, beating well after each addition. Then, mix in the vanilla extract until fully incorporated. The batter should thicken slightly and become homogeneous.
In a separate bowl, whisk together the flour, baking powder, and salt until evenly combined. Gradually fold the dry ingredients into the wet mixture using a rubber spatula, just until combined. Fold in the drained crushed pineapple gently, distributing evenly throughout the batter.
Pour the batter into the prepared cake pan, smoothing the top with a spatula. Place in the oven and bake for about 40 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean. The edges should slightly pull away from the pan.
Remove the cake from the oven and let it cool in the pan for 10 minutes. Then, transfer to a cooling rack and cool completely before serving. The final cake should be moist with a dense crumb and a slightly glossy surface.
