Make cake: Preheat oven to 350°F. Grease three 8-inch-diameter cake pans with 1 1/2-inch-high sides. Line bottoms with waxed paper. Melt chocolate in top of double boiler over simmering water; stir until smooth. Remove from over water and cool to barely lukewarm.
Using electric mixer, cream butter in large bowl until light and fluffy. Gradually add 1 1/4 cups sugar, beating until smooth. Beat in egg yolks 1 at a time. Mix in vanilla. Stir in chocolate, then peanuts. Sift flour over batter and gently fold in. (Batter will be very thick.)
Using clean dry beaters, beat whites with cream of tartar in another large bowl to soft peaks. Gradually add remaining 1/4 cup sugar and beat until stiff but not dry. Fold 1/2 of whites into batter to lighten. Gently fold in remaining whites. Divide batter among prepared pans. Bake until tester inserted in centers comes out clean and tops are crusty, 25 to 30 minutes. Cool in pans on racks 10 minutes. Run small sharp knife around pan sides to loosen, if necessary. Turn out onto racks. Peel off paper. Cool to room temperature. (Cakes can be prepared 2 days ahead. Wrap tightly and refrigerate.)
Make buttercream: Using electric mixer, beat yolks in bowl until pale yellow and slowly dissolving ribbon forms when beaters are lifted, 5 minutes. Meanwhile, stir sugar and water in heavy medium saucepan over low heat until sugar dissolves. Increase heat and boil without stirring until candy thermometer set in syrup registers 234°F. to 240°F. (soft-ball stage).
Beat hot syrup into egg yolks in slow steady stream. Continue beating until thick and cool, about 10 minutes.
Melt chocolate in top of double boiler over simmering water; stir until smooth. Remove from over water and let stand until cool but still liquid. Gradually beat butter into yolk mixture 1 tablespoon at a time. Add chocolate and stir to combine. Transfer 2 cups buttercream to small bowl; stir in chopped Snickers bars.
To assemble cake: Place one cake layer on platter top side down. Spread half of Snickers buttercream over. Top with second cake layer. Spread remaining Snickers buttercream over. Top with third cake layer. Spoon 1 cup plain buttercream into pastry bag fitted with medium star tip. Frost top and sides of cake with remaining buttercream. (Can be assembled 2 days ahead. Cover with cake dome and refrigerate.) Bring cake to room temperature before serving.