Preheat oven to 350 degrees F. Grease and lightly flour two 9-inch-round baking pans or one 13 x 9-inch baking pan.
For Cake: Combine flour, baking soda and salt in small bowl. Beat sugar, butter and vanilla extract in large mixer bowl. Add eggs; beat for 1 minute. Beat in melted chocolate. Beat flour mixture into creamed mixture alternately with milk. Spoon and spread into prepared baking pan(s).
Bake for 25 to 30 minutes (13 x 9- inch 30 to 32 minutes) or until wooden pick inserted in center comes out clean. Cool for 20 minutes; invert round cakes onto wire rack(s) to cool completely.
Frost with Creamy Chocolate Frosting.
For Creamy Chocolate Frosting: Microwave butter and chocolate in small, uncovered, microwave-safe mixer bowl on High (100%) power for 45 seconds; stir. Sections may retain some of their original shape. If necessary, microwave at additional 10- to 15-second intervals, stirring just until smooth; cool to room temperature.
Beat 1 cup powdered sugar, vanilla extract and salt into chocolate mixture until creamy. Gradually beat in remaining powdered sugar alternately with milk until smooth.