Sift flour, baking powder, and salt in a mixing bowl. Cut in butter until mixture resembles coarse pebbles. Lightly stir in banana pur e to make a damp dough. Turn mixture out onto a floured surface. Roll or pat to a 1-inch thickness.
Place rounds on an ungreased baking sheet.
Bake until golden brown, about 30 minutes. Combine cream and brown sugar in a large saucepan. Cook over moderate heat, stirring constantly, until slightly thickened, about 10 to 12 minutes. Allow to cool 10 minutes. Stir rum, banana liqueur, and sliced bananas into warm sauce.