1. In a large saucepan, combine the brown sugar and water and bring to a boil. Reduce heat to low and stir in 1 tablespoon of butter and 1/2 teaspoon of vanilla. Cover while preparing the batter.
2. In a medium bowl, combine the flour, white sugar, baking powder and salt. Cut in 1/3 cup of butter using a fork until the mixture has lumps no larger than crumbs. Make a well in the middle and pour in the milk and 1 teaspoon of vanilla. Stir just until all of the dry mixture is moistened.
3. Return the sugar mixture to a boil. Drop large spoonfuls of the batter into the syrop. Cover and simmer over medium heat for 15 minutes or until a toothpick inserted into the largest dumpling comes out clean. Serve warm.