Cake
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FILLING
SACHER GLAZE
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Position a rack in the center of the oven and preheat to 350° F.
Butter a 9 x 2 1/2 inch springform pan and line the bottom with a parchment or greased waxed paper circle.
With an electric mixer on low speed (or with a stationary mixer fitted with the paddle attachment), beat the butter for 1 minute, or until light. Add the confectioners' sugar and beat for 2 minutes longer. Add the egg yolks two at a time, beating for 10 seconds between additions, or until absorbed by the butter. Scrape down the beaters and sides of the bowl and beat for 1 minute longer, or until smooth. Add the melted chocolate and mix until combined.
Whip the egg whites with a pinch of salt until they form soft peaks. With the machine running, add the superfine sugar, about 2 tablespoons at a time, and beat until the egg whites are stiff and glossy. With a rubber spatula, fold 1/2 the egg whites into the batter. Transfer the flour to a strainer and sift it over the batter as you fold it in along with the remaining beaten egg whites.
Transfer the batter to the prepared cake pan, smooth the top, and set the pan on a larger baking sheet (to catch the drips). Bake for 40 to 45 minutes, or until a tester inserted in the center comes out dry.
Cool the cake to room temperature in the pan on a wire rack. Run a knife around the cake to loosen it from the sides, then unlock the springform and lift the cake out of the ring.
Turn the cooled cake upside down onto a cardboard round cut slightly smaller than the diameter of the cake. Remove the metal base and peel off the paper. With a serrated knife, split the cake horizontally in two and set aside the top layer.
In a small saucepan, combine the sugar with 1/4 cup water and bring to a boil, stirring. Remove from the heat and add 2 tablespoons of the rum.
Puree the apricot preserves in a blender with 1 tablespoon of water and strain out the chunks by passing the puree through a small sieve. Transfer the preserves to a small saucepan and bring them to a boil over low heat, stirring. Boil for 2 minutes, or until thickened, then remove from the heat and add the remaining tablespoon of rum.
With a pastry brush, soak the cake layer on the cardboard with the sugar syrup (be generous or the cake will be dry). Spread 1/3 of the warm apricot preserves over the syrup and top it with the second cake layer. Brush the second layer with the remaining sugar syrup and brush the top and sides with the remaining apricot preserves. Set the cake on a cooling rack or an icing grid set over waxed paper to catch the drips.
Bring the sugar and 1/2 cup water to a boil in a small saucepan and cook until a candy thermometer registers 220° F. Add the chocolate, stir, and cook until a candy thermometer registers 230° F. (the "thread" stage). Remove the saucepan from the heat and stir until smooth.
Pour the hot glaze back and forth over the top and sides of the cake. Be generous as you pour so that the sides get covered, because the glaze can't be moved once it is on the cake. If there are any unglazed patches on the sides of the cake, use a small offset spatula to patch the nude spots with more glaze.
Let the cake stand for 1 hour before transferring it to a plate or platter.
Keep at room temperature, under a cake dome or an inverted large mixing bowl. Refrigerate only after a couple of days, but bring the cake back to room temperature before serving.