Melt 2 teaspoons butter in a large nonstick skillet over medium heat. Add plums, and cook 3 minutes. Add 1/2 cup sugar, cardamom, and dash of salt. Cook 10 minutes or until plums are tender, stirring frequently. Remove plums from pan using a slotted spoon. Bring cooking liquid to a boil. Cook 5 minutes or until liquid is very thick (consistency of jam).
While the cooking liquid reduces, arrange plums in bottom of a 9-inch round cake pan coated with cooking spray. Pour reduced cooking liquid over plums. Let cool.
Preheat oven to 350°.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, and 1/4 teaspoon salt, stirring well with a whisk. Beat 1/4 cup butter and remaining 3/4 cup sugar with a mixer at medium speed until fluffy. Add eggs, one at a time, beating well after each addition. Add flour mixture and buttermilk alternately to sugar mixture, beginning and ending with flour mixture. Beat in amaretto.
Pour batter over plums, spreading batter evenly. Bake at 350° for 50 minutes or until a wooden pick inserted in center comes out clean. Let cool 10 minutes. Run a knife around outside edge. Place a plate upside down on top of cake. Invert cake onto plate; cool.