Preheat the oven to 350 degrees F.

Coat 3 (9-inch) cake pans with cooking spray; dust lightly with flour. Set aside.

Beat butter and sugar at medium-high speed with an electric mixer until fluffy. Add egg yolks, 1 at a time, beating until blended after each addition. Beat in sweet potatoes and next 6 ingredients, adding each ingredient 1 at a time. Add pecans and 3 cups flour, beating just until blended.

Beat egg whites in a separate bowl at high speed with an electric mixer until stiff peaks form; fold into batter. Spoon batter evenly into prepared pans.

Bake for 25 minutes or until wooden pick inserted in center comes out clean. Cool in pans on wire racks 10 minutes; remove and cool completely on wire racks.

Spread Coconut Filling evenly between cake layers. Gradually pour about 1/2 cup Caramel Frosting on top of cake, spreading over top and sides with a small spatula. Place cake in refrigerator. Chill remaining Caramel Frosting 45 minutes. Pour another 1/2 cup Caramel Frosting on cake, spreading over top and sides. Repeat procedure with remaining frosting, using 1/2 cup frosting at a time and chilling every 15 minutes. Store cake in refrigerator.

Coconut Filling:

Combine first 3 ingredients in a heavy 2-quart saucepan; gradually stir in milk, and cook, stirring constantly, over medium heat 3 minutes or until thickened.

Stir about one-fourth of hot milk mixture gradually into egg; add egg mixture to remaining hot milk mixture, stirring constantly. Return to a boil, and cook, stirring constantly, 1 minute or until thickened. Remove from heat; stir in coconut and vanilla. Place heavy-duty plastic wrap directly on warm filling. Cool completely; chill 1 hour.

Caramel Frosting:

Whisk together cream cheese and cream in a small bowl until smooth.

Cook sugar and 2/3 cup water in a heavy 3 1/2-quart saucepan over medium-low heat, stirring constantly, 5 minutes or until sugar dissolves. Increase heat to high, and bring mixture to a boil without stirring. Using a pastry brush dipped in hot water, wash down any sugar crystals on sides of pan. Cook, without stirring, 10 minutes or just until syrup turns a deep amber color.

Whisk in butter gradually; gradually whisk in cream cheese mixture until smooth. Remove from heat; cool 10 minutes, whisking occasionally.