Preheat oven to 350°F.
For Cake, in large mixing bowl, beat egg yolks at high speed with electric mixer until light and fluffy.
Gradually add granulated sugar, beating until mixture is thick and light colored.
On low speed add flour and 3 tablespoons cocoa; mix well.
In another mixing bowl, using clean beaters, beat egg whites until soft peaks form.
Carefully fold egg whites into chocolate mixture.
Spread in 15 x 10 x 1 inch greased and waxed-paper-lined jelly-roll pan.
Bake 15 minutes or until cake springs back when lightly touched.
Cake will fall slightly as it cools.
Let cake cool in pan 15 minutes; loosen edges with knife.
Turn cake out onto piece of waxed paper dusted with confectioners' sugar.
Carefully remove waxed paper lining.
Cover cake with dish towel; cool completely.
For Filling, melt caramels with cream in heavy saucepan, stirring constantly, until smooth.
Remove from heat and stir in rum.
Cool to room temperature.
When cool, fold in whipped topping.
Spread over cake and sprinkle with 1/3 cup nuts.
Roll up, starting from short end.
Place in freezer while preparing frosting.
For Frosting, beat butter until fluffy.
Alternately add sugar and 1/3 cup cocoa with milk, beating until frosting is smooth and fluffy.
Remove cake from freezer.
Slice 1-inch piece of cake roll off end of log.
Spread frosting on one side of log and press slice, cut side up, in place.
Frost entire cake and stump.
Swirl ends of log and flat side of stump to resemble cut section of log.
Run tines of fork over length of log to resemble bark.
Sprinkle with 1/4 cup nuts.
Refrigerate at least 2 hours before serving.