Process pecans in a food processor until ground; set aside.
Beat butter and shortening at medium speed with an electric mixer until creamy; gradually add sugar, beating well. Add vanilla, beating until blended. Add egg yolks, 1 at a time, beating until blended after each addition.
Combine flour, soda, and pecans; add to sugar mixture alternately with buttermilk, beginning and ending with flour mixture. Beat at low speed until blended after each addition.
Beat egg whites until stiff peaks form; fold into batter. Pour into a well-greased and floured 15- x 10-inch jellyroll pan.
Bake at 350° for 20 minutes or until a wooden pick inserted in center comes out clean. Cool in pan on a wire rack 10 minutes; remove from pan, and cool on wire rack.
Line a 3-quart mixing bowl (8 1/2 inches across) with plastic wrap.
Cut cake lengthwise into 2-inch strips; line prepared bowl with cake strips, reserving remainder. Spread Chocolate Mousse over cake in bowl; cover and chill 1 hour.
Pour White Chocolate Mousse into bowl over chocolate layer; cover and chill 1 hour. Cover with remaining strips. Cover and chill at least 8 hours.
Invert bombe onto a cake plate, and spread with ganache. Garnish, if desired.