Weigh or lightly spoon flour into dry measuring cups; level with a knife.
Combine flour, 2 tablespoons granulated sugar, brown sugar, baking powder, 1/4 teaspoon salt, and cardamom in a medium bowl, stirring well with a whisk.
Cut in 4 tablespoons butter with a pastry blender or two knives until mixture resembles coarse meal.
Combine milk, vanilla, and egg in a bowl, stirring with a whisk.
Add milk mixture to flour mixture, and stir until just combined.
Spoon batter into a 9-inch round metal cake pan coated with cooking spray. Arrange plums in a circular pattern over batter.
Combine remaining 2/3 cup granulated sugar, remaining 1/8 teaspoon salt, lemon rind, and allspice in a small bowl, stirring well.
Place remaining 3 tablespoons butter in a microwave-safe bowl. Microwave at HIGH 30 seconds or until butter melts. Stir into sugar mixture.
Sprinkle plums evenly with sugar mixture.
Bake at 425 for 35 minutes or until browned and bubbling. Cool in pan 1 hour on a wire rack.
