If you like frangipane (cream fillings made from or flavored with almonds), this is the dessert for you. Plums and pluots, like all stone fruits, have an affinity for almonds, so this pudding-like cake is based on almond flour (also called almond meal). The cake base is topped with slices of fruit that have been lightly cooked to make a thick syrup. Composed in individual custard cups, these desserts are comfort food at their best. Serve warm with whipped cream or vanilla ice cream.
Position a rack in the lower third of the oven and preheat to 350 degrees F. Butter the bottom and sides of four 1-1/2-cup ramekins and set aside.
Place 1-1/4 sticks (10 tablespoons) of butter in the bowl of an electric mixer and add 2/3 cup of the sugar. Beat until the mixture is smooth. Add the eggs and almond extract, and beat again. Add the almond flour and mix until combined. Divide the batter among the 4 prepared ramekins, about 1/2 cup of batter for each.
Cut the plums (or pluots) in half through the stem end, discard the pits, and slice each half into 4 wedges.
Heat 1 tablespoon of butter in a large skillet and add the star anise, nutmeg, and the remaining 2/3 cup of sugar. Cook over medium heat until the sugar melts, stirring frequently. Add the plums and cook, stirring occasionally, until the fruit just begins to soften, 4 to 6 minutes. Remove the pan from the heat. Arrange the plums on top of the puddings and spoon the syrup over the fruit.
Bake until the almond cake is golden and the plums are tender, 35 to 45 minutes. Cool for 15 minutes, then serve the pudding cakes warm with whipped cream or ice cream, if desired.