Preheat oven to 350 degrees. Grease and flour 2 9-inch cake pans. Line bottom of pan with parchment paper.
In large bowl or standing mixer, cream butter until light and fluffy. Add sugar and beat until creamy. Add eggs, one at a time, beating well after each addition. Stir in melted chocolate.
In separate bowl, combine four and salt. Add buttermilk and chocolate mixture, alternating. Stir in vanilla.
In small bowl, dissolve baking soda in vinegar. Slowly add this to the chocolate mixture. Mix just until blended. Do not over-mix.
Pour batter into prepared pans and bake for 30-35 minutes or until toothpick inserted in center comes out clean. Cool in pans 10 minutes then remove from pans. Transfer to wire racks and cool completely before frosting.
In large mixing bowl, cream butter until light and fluffy. Slowly add sugar, 1/2 cup at a time, beating well between additions. Stir in chocolate and vanilla. If necessary, thin frosting with 1-2 tsps. half-and-half.