Step 1

Place the chocolate in a medium bowl, pour the boiling water over top, and stir until melted. Let cool. Stir in the vanilla.

Step 2

Position a rack in the center of the oven. Preheat the oven to 350°F (325°F for a convection oven). Grease three 9- by 1½-inch round cake pans, two 8-inch by 2-inch square pans, or one 13- by 9-inch pan, line with parchment paper or waxed paper, and grease again.Sift together the flour, baking soda, and salt.

Step 3

In a large bowl, beat the butter on low speed until smooth, about 2 minutes.

Step 4

Increase the speed to medium, gradually add the sugar, and beat until light and fluffy, about 4 minutes.

Step 5

Beat in the egg yolks, one at a time.

Step 6

Stir in the chocolate.

Step 7

Add the flour mixture alternately with the milk (4 portions for the flour; 3 portions for the milk) beginning and ending with the flour, until smooth. The batter will be rather thick.

Step 8

In a medium bowl, beat the egg whites on low until foamy, about 1 minute. Increase the speed to medium and beat until stiff but not dry, 5 to 8 minutes.

Step 9

Fold one fourth of the egg whites into the batter, then fold in the remaining whites.

Step 10

Divide the batter equally between the prepared pans. Bake until a toothpick inserted in the center comes out clean and the cake springs back when lightly touched, 30 to 35 minutes for 9-inch rounds; 45 to 50 minutes for the 8-inch squares; and 45 to 50 minutes for a 13- by 9-inch.

Step 11

Let cool in the pans for 10 minutes, then remove the cakes to wire racks and let cool completely, at least 1½ hours. The cake can be wrapped in plastic wrap and stored at room temperature for up to 2 days.

Step 12

In a medium saucepan, cook the milk, sugar, butter, egg yolks, and salt over medium heat, stirring constantly, until bubbly and thickened or 170°F, about 12 minutes.

Step 13

Remove from the heat and add the vanilla. Stir in the coconut and pecans. Let cool, stirring occasionally, until thick enough to spread, about 30 minutes.

Step 14

Place a cake layer on a serving plate, spread the top with one third of the frosting. Arrange a second cake layer on top, spread with one half of the remaining frosting, top with the remaining cake layer, and spread the remaining frosting on top. Or for a sheet cake, spread the frosting over the top and sides; or cut the cake lengthwise into thirds and layer. Store in an airtight container at room temperature for up to 5 days. Do not freeze.