Brush the ladyfingers with rum and use them to line the bottom and sides of a 10 inch spring form pan.
In a medium saucepan over low heat, melt butter. Remove from heat and add 24 ounces of chocolate chips; stir until melted. Cool slightly, then beat egg yolks into the mixture, one at a time, until smooth.
In a separate bowl, beat the egg whites with an electric mixer until they form stiff, but not dry peaks. Fold the whites into the chocolate mixture and pour into the lined pan. Chill in refrigerator for 6 hours.
In a large bowl, whip the cream with an electric mixer until thick. Blend in sugar and vanilla, and whip until stiff peaks form. Invert the chilled cake onto a serving platter and remove the sides and bottom of the pan.
Spread a layer of whipped cream over the entire cake, and pipe the remaining whipped cream into a decorative pattern of your choice. In the top of a double boiler, melt the 1/2 cup chocolate chips with the oil. Cool, then drizzle over finished cake. Refrigerate until serving.
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