Grease a 9×13 pan and line it with parchment or wax paper. Grease that as well. Preheat oven to 325.
Reserve 6 apricot halves, and puree the rest in the food processor.
Sift the flour, baking powder and salt together. Set aside.
Separate the eggs, making sure to get absolutely no yolk in the white. Set aside and have a beater ready.
Cream the butter and sugar together, add the vanilla, then add the egg yolks one at a time. Add about a third of the apricot puree, mix, add about a third of the flour, mix, add more puree, the remainder of the flour, then rest of puree. Mix thoroughly.
In a separate bowl, beat the egg whites until stiff peaks form. Take a little of the batter and add it to the egg whites, mix slightly. Fold this mixture carefully into the batter, you will have white streaks remaining. That’s okay.
Take the 6 reserved apricot halves and put the cut side down in the prepared pan. Carefully pour the batter over the apricots, smoothing it out as you go, but not disturbing the apricots.
Bake in the oven for about 30 minutes or until a toothpick comes out clean.
Remove from the oven, and cool in the pan on a wire rack for about 1 minute. Get a nice plate, and turn the cake out on to it, so the bottom of the cake is right-side up.
You can sprinkle with powdered sugar if you want, or pour some milk icing on. Serve warm.
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