Combine blackberries, water, and 2 1/2 cups sugar in a large Dutch oven; stir well. Cook over medium heat until mixture comes to a boil.
Combine milk, 1 cup sugar, butter, eggs, and vanilla in a large mixing bowl; mix well. Combine flour and baking powder, stirring well. Gradually add flour mixture to milk mixture, stirring lightly until dry ingredients are moistened and a soft dough forms.
Drop dough by teaspoonfuls into boiling blackberry mixture. Cook 2 to 3 minutes or until dumplings rise to surface and center of dumplings test done when pierced with a wooden pick. Transfer dumplings to individual serving bowls, using a slotted spoon. Spoon blackberry mixture over dumplings, and serve warm with vanilla ice cream.