Preheat your oven to 375°F (190°C). In an ungreased 9-inch square baking pan, mix the melted butter and brown sugar until evenly combined.
Drain the canned pineapple, reserving 1/3 cup of the juice. Arrange 9 pineapple slices in a single layer over the brown sugar mixture, and sprinkle the pecans on top. Refrigerate any extra pineapple for another use.
In a mixing bowl, whisk the egg yolks until thick and pale yellow. Gradually add sugar while whisking, then stir in the reserved pineapple juice and vanilla extract.
In a separate bowl, sift together the flour, baking powder, and salt. Gradually fold this dry mixture into the wet batter until smooth.
Using clean beaters, whip the egg whites on high speed in a small bowl until stiff peaks form. Gently fold the egg whites into the batter, taking care not to deflate it.
Pour the batter evenly over the pineapple and pecans in the pan. Smooth the top and bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes. Then, invert it carefully onto a serving plate. Place a maraschino cherry in the center of each pineapple ring for a pop of color.
Slice, serve, and savor! You can optionally top it with a dollop of whipped topping for extra indulgence.