Preheat your oven to 350°F (175°C) and generously butter a 9-inch round cake pan to prevent sticking.
Melt the butter in a heavy pan over medium heat until it turns golden and emits a faint nutty aroma. Carefully sprinkle the brown sugar evenly over the melted butter, then cook until the mixture bubbles and thickens into a caramel, about 2-3 minutes.
Pour the caramel into the prepared cake pan, spreading it evenly across the bottom. Arrange the pineapple rings in a single layer on top of the caramel, pressing them gently into the caramel to help them stay in place.
In a mixing bowl, whisk together the eggs, vanilla extract, vegetable oil, and salt until smooth and well combined. Gradually add the sifted flour, folding gently until the batter is just combined and smooth.
Pour the batter carefully over the pineapple slices in the pan, smoothing the top with a spatula. Be gentle to avoid disturbing the fruit arrangement.
Bake the cake in the preheated oven for about 35 minutes, or until the top is golden and a toothpick inserted into the center comes out clean.
Once baked, remove the cake from the oven and let it cool for 10 minutes. Then, place a serving plate over the pan and carefully invert the cake onto the plate, revealing the caramelized pineapple topping.
Allow the cake to cool slightly before slicing. Serve warm or at room temperature to enjoy the sticky caramel, juicy pineapple, and tender crumb.
