In an ungreased 9-inch square baking pan, combine the melted butter and brown sugar, spreading it into an even layer. Arrange the 9 pineapple slices in a single layer over the sugar mixture.
In a medium bowl, whisk together the flour, baking powder, and salt; set aside.
In a large bowl, beat the egg yolks on medium speed until thick and pale yellow, about 3 minutes. Gradually add the sugar, beating well until completely incorporated. Add the pineapple juice and vanilla extract, and blend to combine.
Reduce the mixer speed to low, add the flour mixture, and beat until just combined.
In a clean medium bowl with clean beaters, beat the egg whites on medium-low speed until frothy, then gradually increase to medium-high speed and beat until stiff peaks form. Gently fold the egg whites into the egg yolk mixture until no white streaks remain.
Spoon the batter into the pan, spreading it evenly over the pineapple slices. Bake until a toothpick inserted in the center comes out clean, 28 to 32 minutes. Allow to cool for 10 minutes, then invert the pan onto a serving dish. Place a maraschino cherry in the center of each pineapple slice.
Use a 20-ounce can of sliced pineapple for this recipe - you will have enough slices for the cake, and enough juice needed for the batter, as well.