Paint outside of the ladyfingers with rum and place flat side down, around the sides and on the bottom of a 10 inch springform pan.
Melt butter in medium pan; remove from heat and add 24 oz of the chocolate bits.
Stir until melted; cool slightly.
Beat the egg yokes into the mixture one at a time until all are incorporated into the chocolate.
Beat egg whites until they form stiff, not dry, peaks.
Fold the whites into the chocolate mixture and pour into springform pan.
Chill for at least 6 hours.
Whip the cream until thickened; add sugar and vanilla.
Continue whipping until very stiff.
Turn the cake onto a serving platter, removing pan sides and bottom.
The lady fingers will now be on top.
Spread whipped cream over the entire cake.
Melt the remaining chocolate chips with the oil in double boiler.
Cool completely.
Dribble sauce down the sides of the cake.