To prepare soup, heat oil in Dutch oven over medium heat. Add onion; cook 5 minutes, stirring frequently. Add aniseed, cumin, and garlic; cook 2 minutes, stirring constantly. Stir in broth, 3 cups water, 1/4 teaspoon salt, and beans; bring to a boil. Reduce heat to low; simmer 45 minutes. Place half of bean mixture in blender; process until smooth. Pour pureed mixture into a large bowl. Repeat procedure with remaining bean mixture. Return pureed mixture to pan.
To prepare dumplings, lightly spoon masa into a dry measuring cup; level with a knife. Combine masa, baking powder, and 1/4 teaspoon salt. Cut in butter with a pastry blender until mixture resembles coarse meal. Stir in water and cilantro. Divide dough into 10 portions, shaping each into a ball (dust hands with masa to prevent sticking). Make a small indention in each dumpling. Bring bean mixture to a boil. Add dumplings. Reduce heat; simmer 10 minutes, stirring frequently. Stir in vinegar.