Stir together 1/2 cup beef broth and flour in small cup until smooth.
Melt butter in 6-quart large, deep pot over medium-high heat. Add onions; sauté 5 minutes. Add beef, green beans, remaining beef broth, the water, mustard, salt and pepper. Simmer, covered, 5 minutes.
For dumplings, combine buttermilk baking mix and dill in bowl; stir in milk just until moistened.
Stir flour mixture, then stir into stew; cook until thickened, 1 minute.
Drop about 9 dumplings, about 1 tablespoon each, on top of simmering stew. Cook, uncovered, 10 minutes. Then cover and cook 10 minutes.