PREHEAT THE OVEN to 350°F. Butter a 9 × 5-inch loaf pan and dredge it with polenta, shaking out the excess.

TO MAKE THE CAKE: In a stand mixer or with a strong hand mixer, cream the butter, sugar, and salt together until light and fluffy, Add the vanilla. Add the eggs and egg yolks, one at a time, completely incorporating each one before adding the next. Sift in the flour, polenta, and baking powder and mix well. Pour the batter into the pan.

BAKE FOR 50 TO 55 MINUTES, or until the top springs back and a skewer inserted in the center comes out clean. Run a knife around the pan to release the cake and invert it onto a rack. Allow to cool completely.

TO PREPARE THE FRUIT: In a medium saucepan, combine the crème de cassis with the apple juice and sugar. Stir over low heat until the sugar has dissolved. Increase the heat and bring the mixture to a boil. Add the plums, nectarines, and blackberries and reduce the heat to a simmer. Cover and simmer for 8 to 10 minutes, or until the fruits are tender. Remove the lid and simmer for 6 to 7 minutes more, stirring occasionally, until the syrup has reduced to coating consistency and the softened fruits are glazed with it.

CUT THE CAKE into 1-inch slices, place on individual dessert plates, and spoon some of the warm fruit and syrup over each. Top with a dollop of sweetened mascarpone and serve.