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Step 1
Place an egg separator over a small bowl. Crack open 1 egg over the egg separator to seperate the yolk from the white; then separate the other egg. (Save the whites for another recipe.) In a small bowl, place the yolks. Beat the egg yolks with a fork or wire whisk until mixed. Stir in 1 1/2 cups milk; set aside.
Step 2
In a 2-quart saucepan, stir 1/3 cup granulated sugar, the cornstarch and 1/8 teaspoon salt until mixed. Gradually stir egg mixture into sugar mixture. Cook over medium heat, stirring constantly, until mixture thickens and boils. Boil and stir 1 minute; remove from heat. Stir in 2 teaspoons vanilla. Press plastic wrap on surface of filling to prevent a tough layer from forming on top. Refrigerate at least 2 hours until set but no longer than 24 hours. While filling is chilling, continue with recipe.
Step 3
Heat the oven to 350°F. Spray just the bottom of a 9-inch round cake pan with baking spray with flour.
Step 4
In a large bowl, beat all cake ingredients with an electric mixer on low speed 30 seconds, stopping frequently to scrape batter from side and bottom of bowl with a rubber spatula. Beat on high speed 3 minutes, stopping occasionally to scrape bowl. Pour batter into the pan; use a rubber spatula to scrape batter from bowl, spread batter evenly in pan and smooth top of batter.
Step 5
Bake about 35 minutes or until a toothpick inserted in the center comes out clean. Cool cake in pan on a cooling rack 20 minutes, then remove onto cooling rack to finish cooling completely, about 1 hour.
Step 6
In a 1-quart saucepan, melt 3 tablespoons butter and the chocolate over low heat, stirring occasionally. Meanwhile, in 1-cup glass measuring cup, microwave the water uncovered on High 15 to 30 seconds or until hot. Remove chocolate mixture from heat. Stir in the powdered sugar and 3/4 teaspoon vanilla. Stir in 3 tablespoons hot water. Stir in additional water, 1 teaspoon at a time, until icing is smooth and thin enough to spread.
Step 7
To split cake horizontally in half, mark middle points around side of cake with toothpicks. Using toothpicks as a guide, cut through the cake with a long, sharp knife, using a back-and-forth motion. On a serving plate, place bottom layer with the cut side up. Spread filling over bottom layer. Top with top of cake, cut side down.
Step 8
Spread glaze over top of cake, using a metal spatula or back of a spoon, letting some glaze drizzle down side of cake. Refrigerate uncovered until serving. Store any remaining cake covered in the refrigerator.