Make cake:

Preheat oven to 350F. Line bottom of a buttered 9- by 2-inch round cake or springform pan with a round of wax paper and butter paper. Dust pan with flour, knocking out excess.

In a bowl with an electric mixer cream butter with 2/3 cup sugar until light and fluffy. Onto a sheet of wax paper sift together flour, baking powder, and salt. Stir flour into butter mixture alternately with milk in batches, beginning and ending with flour. Stir in vanilla and blend batter until just combined well.

In another bowl with clean beaters beat egg whites until they hold soft peaks. Beat in remaining 1/3 cup sugar gradually and beat meringue until it holds stiff peaks. Stir one fourth meringue into batter to lighten and fold in remaining meringue gently but thoroughly.

Spread batter evenly in prepared pan and bake in middle of oven 30 to 35 minutes, or until cake begins to pull away from side of pan and a tester comes out clean. Cool cake in pan on a rack 10 minutes. Invert cake onto rack and cool completely. Cake may be made 1 day ahead and kept at room temperature, tightly wrapped.

Make filling:

In a dry heavy skillet cook 1/3 cup sugar over moderate heat, undisturbed, until it begins to melt. Cook, stirring with a fork, until melted completely and a light caramel. Add macadamia nuts and cook, stirring, until nuts are coated well and caramel is deep golden. Pour praline onto a sheet of foil and cool completely. Break praline into pieces and in a food processor grind fine. (Do not puree to a paste.)

In a small saucepan whisk together remaining 3 tablespoons sugar, egg yolks, milk, and cornstarch. Bring pastry cream to a boil over moderate heat, whisking, and cook over low heat, whisking constantly, 2 minutes. Whisk in vanilla. Transfer pastry cream to a bowl and chill until cold, its surface covered with plastic wrap. (Pastry cream will be very stiff.)

In a bowl beat heavy cream until it just holds stiff peaks. Whisk pastry cream to loosen and whisk in praline. Fold in whipped cream and chill while making frosting.

Make frosting:

In a metal bowl set over a pan of simmering water whisk together frosting ingredients until mixture is warm and sugar is dissolved. With a portable electric mixer on high beat frosting 6 to 7 minutes, or until thick and fluffy. Remove bowl from heat and beat frosting until cooled slightly.

Assemble cake:

With a long serrated knife cut cake horizontally into 3 layers. Spread filling between layers on a cake plate and spread cake with frosting. Coat cake with coconut. Cake may be made 6 hours ahead and chilled, covered loosely. Garnish cake with macadamia nuts.