Preheat the oven to 350°. Coat the inside of a 10-inch springform pan with 1/4 teaspoon of the butter; reserve the rest.
In a food processor, combine the flour, almonds and 2/3 cup of the sugar and process until a coarse powder forms. Add the eggs, oil, baking powder, vanilla and remaining butter; process just until incorporated. Add the milk and process just until the batter is smooth. Pour the batter into the prepared pan; in should be about 3/4 inch deep in the pan.
Using the tip of a sharp knife, remove the pit from the stem end of each plum. Rinse the whole pitted plums well in cold water and, while they are still wet, roll them in the remaining 3 tablespoons of sugar. Push the plums down into the cake batter until half immersed, making sure to space them evenly.
Set the pan on a cookie sheet. Bake in the center of the oven for 40 minutes, or until the cake is puffed and browned. Let cool on a rack until lukewarm.
Mix the plum jam and brandy and brush the glaze over the lukewarm cake. Remove the springform pan and cut the cake into 6 wedges; each serving should contain a plum. Serve lukewarm or at room temperature.
Juicy, ripe plums need an equally fruity, plummy sweet wine. Muscat, such as Kiona Late Harvest from Washington State or Alderbrook Kunde Vineyard Muscat de Frontignan from California, has just the right amount of sweetness and aromatic flavor.