Bresse Farmhouse Chocolate Cake

Simmer cream until reduced by half, about 20 minutes.
Preheat the oven to 400F (200C).
Lightly butter an 8-inch springform pan.
In a double boiler, melt 4 ounces of the chocolate with 1/4 pound of the butter, cut into small pieces.
In a medium bowl, blend the flour and 13 cup of the sugar.
Add the eggs and mix well.
Add the melted chocolate and butter to the bowl and, with an electric mixer, beat at high speed for about 5 minutes, until the batter is smooth and forms a ribbon when the beaters are lifted.
Pour the batter into the prepared pan (it will be about 1 inch deep) and bake for 15 to 20 minutes, until the cake is set and a toothpick inserted in the center comes out dry.
Unmold the cake onto a rack and let it cool; it will fall to about half its original height.
Meanwhile, in a double boiler, melt the remaining 3 ounces of chocolate with the remaining 1 teaspoon butter.
In a small heavy saucepan, bring the reduced cream to a boil, then whisk it vigorously into the chocolate.
Continue whisking until smooth and glossy.
Place sheets of waxed paper under the cake and cooling rack.
Pour the frosting over the top of the cake, using a metal spatula to spread the frosting evenly over the top and sides.
After the frosting has hardened slightly, about 5 minutes, use a long straight knife to mark the top in a crisscross pattern.
Mix the cocoa with the remaining 1 tablespoon sugar and sprinkle it decoratively over the cake before serving.