Stir together the flour, salt, white sugar, and baking powder.
Separate the eggs, the whites in one bowl, and the yolks in another. Beat the whites until stiff.
Beat the egg yolks until smooth and lemony yellow. Stir in the remaining pineapple juice, vanilla, and remaining melted butter. Add this mixture to the flour mixture, then gently fold in the egg whites.
Pour the batter over the top of the brown sugar and pineapple rings layer.
Bake for 25 to 30 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Remove from the oven and let the cake cool in the pan for 10 to 15 minutes before flipping it.
Flip the cake by covering the pan tightly with a serving dish and invert so that the pineapple side faces up.
Cut and serve.