In a saucepan over medium heat, combine 1 cup brown sugar, chocolate and 1 cup milk and whisk until chocolate melts and ingredients come together. Remove from heat and cool.
In a medium bowl, whisk together flour, baking soda and salt and reserve. In bowl of an electric mixer on medium speed, beat butter until creamy, about 1 minute.
Add remaining 1 cup brown sugar and beat until light and fluffy, about 2 minutes. Add eggs, one at a time, beating well after each addition. Stir remaining 1/2 cup milk and vanilla extract into chocolate mixture. Reduce speed to low and add chocolate mixture and flour mixture in three parts, beginning and ending with chocolate mixture and mixing until just combined.
Pour batter into prepared pans and bake 40 to 45 minutes, until a toothpick inserted in center comes out clean. Remove from oven and cool completely before icing.
marilyn ause's chocolate frosting
Makes enough for one (8-inch) double-layer cake or one (9- by 13-inch) cake.