Preheat oven to 375 degrees. Butter a round 8 1/2-inch by 2 1/2-inch springform pan; line with parchment paper. Melt 2 tablespoons butter; pour into pan. Using a sieve, sprinkle light-brown sugar evenly over the melted butter. Arrange plum halves cut side down on top of the brown sugar, squeezing in as many plums as possible to allow for shrinkage during baking. Fill in the gaps with raspberries; set aside.
Sift together the flour, cinnamon, baking powder, baking soda, salt, and nutmeg; set aside. In an electric mixer fitted with the paddle attachment, cream the remaining 8 tablespoons butter and the sugar until light. Beat in the vanilla extract. Add the egg yolks, one at a time, beating well after each addition. Add half the flour mixture, and beat until combined. Beat in the sour cream. Beat in the remaining flour mixture.
Spoon cake batter on top of plums and raspberries, spreading evenly with a small spatula. Place the pan on a rimmed baking sheet to catch any juices; transfer to the oven, and bake until a cake tester inserted into the cake comes out clean, 60 to 70 minutes. Transfer to a wire rack to cool, about 1 hour. Run a knife around edge of pan to loosen cake. Remove ring; invert onto a serving plate. Serve slightly warm or at room temperature.
We used black plums, but red or Italian plums are just as delicious. Use more or fewer plums depending on their size. You will need an eight-and-a-half-by-two-and-a-half-inch round springform pan.