Rinse plums, pit, and cut into 1/2-inch-thick slices.
Butter and flour a 10-inch cake pan that has a removable rim.
In a bowl, combine 1/2 cup butter, granulated sugar, and almond paste. With a mixer at high speed, beat until mixture is blended, about 2 minutes. Add eggs and beat until fluffy, 2 or 3 minutes. Add 1 cup flour, stir to mix, then beat until well blended.
Scrape batter into cake pan. Arrange plum slices evenly on batter.
Bake in a 350° oven until cake just begins to pull from pan sides and is golden brown, about 45 minutes.
Cool in pan at least 10 minutes. Run a thin-bladed knife between cake and pan rim; remove rim. Dust cake with powdered sugar. Cut into wedges.