For the Cake: Preheat oven to 350°. Place shaved coconut in a single layer in a shallow pan. Place pecans in a second shallow pan. Bake coconut and pecans at the same time 5 to 7 minutes or until coconut is toasted and pecans are lightly toasted and fragrant, stirring halfway through.
Beat butter and shortening at medium speed with an electric mixer until fluffy; gradually add granulated and brown sugars, beating well. Add egg yolks, 1 at a time, beating until blended after each addition. Add vanilla, beating until blended.
Combine flour and baking soda; add to butter mixture alternately with buttermilk, beginning and ending with flour mixture. Beat at low speed just until blended after each addition. Stir in pecans and 1 cup sweetened flaked coconut.
Beat egg whites at high speed until stiff peaks form, and fold into batter. Pour batter into 3 greased and floured 9-inch round cake pans.
Bake at 350° for 23 to 25 minutes or until a wooden pick inserted in center comes out clean. Cool in pans on wire racks 10 minutes; remove from pans to wire racks, and cool completely (about 1 hour).
Prepare Quick Caramel Frosting. Immediately spread frosting between layers and on top of cake. Spread Cream Cheese Frosting over sides of cake; press 3 cups toasted shaved coconut onto sides of cake.
QUICKE CARAMEL FROSTING: Bring first 3 ingredients to a rolling boil in a 3 1/2-qt. saucepan over medium heat, whisking constantly (about 7 minutes).
Stir in cream, and bring to a boil; remove from heat. Pour into bowl of a heavy-duty electric stand mixer. Gradually beat in powdered sugar and vanilla at medium speed, using whisk attachment; beat 8 to 12 minutes or until thickened. Use immediately.
Test Kitchen Tip: Don't panic if you overbeat the frosting. Thin to a spreadable consistency by adding 1 to 2 teaspoons hot water.
CREAM CHEESE FROSTING: Beat butter and cream cheese at medium speed with an electric mixer until creamy. Gradually add powdered sugar, beating at low speed until blended; stir in vanilla.