To poach the apricots: First bring the water and sugar to a boil in a medium-size saucepan. Add the vanilla bean and Sauternes, and reduce the heat so the syrup is at a simmer.

Cut the apricots in half and remove the pits. Add the apricot halves to the syrup and poach for about 10 minutes, until apricots soften. If you use dried apricots, poach them until tender, for 30 to 45 minutes.

Remove from the heat andlet stand until the cake is almost ready to serve. Or you can poach the apricots several days in advance. The longer they stand in the syrup, the more intense their Sauternes flavor.

To make the almond topping for the cake: Melt the 2 tablespoons of butter in a 9 by 2-inch cake pan. Remove from heat and cool briefly. Sprinkle the teaspoon of sugar evenly over the butter, then add the sliced almonds, tilting and shaking the pan to distribute them evenly. Set the pan aside while you make the cake batter.

To make the pistachio and cardamom cake: Position the oven rack in the center of the oven. Preheat the oven to 350 degrees.

In a food processor, pulverize the pistachios with 1/4 cup of the flour as finely as possible.

Beat together the butter and sugar, beating until very light and fluffy, about 5 minutes if you are using an electric mixer. If you are using a hand mixer, stop once or twice to scrape down the sides of the bowl.

Add the eggs, one at a time, beating slowly and stopping the mixer to scrape down any unincorporated batter. After the eggs have been added, the batter may look slightly curdled. This is normal.

Sift together the remaining 3/4 cup flour, baking powder, and salt and stir into the batter. Mix in the pistachio-flour mixture and ground cardamom seeds.

Transfer the batter to the prepared pan by making four or five mounds of batter on top of the almonds. Carefully spread the batter into an even layer, disturbing the almond sugar topping as little as possible.

Bake the cake for 40 minutes, or until a toothpick inserted in the center comes out clean. Remove from the oven and let cool for 15 to 30 minutes. While the cake is cooling, remove the apricots from their liquid, and reduce the liquid by about half, until thick and syrupy.

Use a knife to loosen the sides of the cake from the pan. Wearing oven mitts, invert a serving plate over the cake pan, then simultaneously flip over both the plate and the cake. If necessary, shake gently or tap the upturned bottom of the cake pan to release the cake. Serve with the poached apricots and their syrup.