Heat oven to 350°F Grease and flour one 9-inch round baking pan.
Stir together flour, sugar, cocoa and baking soda in large bowl. Add butter, milk, egg and vanilla. Beat on low speed of mixer until all ingredients are moistened. Beat on medium speed 2 minutes. Pour batter into prepared pan.
Bake 30 to 35 minutes or until wooden pick inserted in center comes out clean. Cool 10 minutes; remove from pan to wire rack. Cool completely.
Stir together sugar, cocoa and cornstarch in medium saucepan; gradually stir in light cream. Cook over medium heat, stirring constantly, until mixture thickens and begins to boil. Boil 1 minute, stirring constantly; remove from heat. Stir in butter and vanilla. Press plastic wrap directly onto surface. Cool completely.
Cut cake into two thin layers. Place one layer on serving plate; spread filling over layer. Top with remaining layer.
SATINY CHOCOLATE GLAZE.
Heat water, butter and corn syrup in small saucepan to boiling. Remove from heat; immediately stir in cocoa. With whisk, gradually beat in powdered sugar and vanilla until smooth; cool slightly.
Pour onto top of cake, allowing some to drizzle down sides. Refrigerate until serving time. Cover; refrigerate leftover cake. 8 servings.