Combine first 3 ingredients in a bowl, stirring well. Pat mixture onto bottom and sides of a lightly greased 11" tart pan. Bake at 350° for 10 minutes.
Beat egg whites at high speed of an electric mixer until soft peaks form. Gradually add 1/3 cup sugar, beating 4 minutes or until thickened. Stir in coconut, sweetened condensed milk, and 1 teaspoon vanilla. Spread coconut mixture over crust in pan.
Melt 1/4 cup butter and unsweetened chocolate in a heavy saucepan over medium-low heat. Remove from heat.
Beat 3 eggs at medium speed until thick and frothy. Gradually add 1/2 cup sugar, salt, and 1 teaspoon vanilla, beating until blended. Stir in melted chocolate mixture. Spoon over coconut mixture in tart pan.
Bake at 350° for 40 minutes. Let cool completely; carefully remove sides of tart pan.
Roast whole almonds on a baking sheet at 350° for 8 to 12 minutes. Let cool. Melt 4 ounces semisweet chocolate in top of a double boiler over hot, not simmering, water. Remove from heat and let cool until chocolate registers 90° on an instant-read thermometer. Add roasted almonds, stirring constantly for 2 to 3 minutes until chocolate begins to set. Remove chocolate-coated almonds and let dry on wax paper.
Bring whipping cream and corn syrup to a boil in a small saucepan. Remove from heat and pour over remaining 6 ounces semisweet chocolate. Let stand 1 minute. Whisk until smooth. Pour chocolate mixture over baked tart. Place chocolate-coated almonds around edge of tart.
Melt white chocolate and shortening in top of double boiler over hot, not simmering, water. Remove from heat and drizzle over tart. Let stand until topping is set.