Add beef to pan; cook 4 minutes, stirring to crumble.
Add onion, 1/2 teaspoon salt, pepper, and garlic; saut 5 minutes or until translucent.
Add cabbage, beet, water, vinegar, and remaining 1/2 teaspoon salt; cook about 10 minutes or until cabbage begins to wilt and liquid almost evaporates. Spoon 1 1/4 cups hash into each of 4 serving bowls; top each serving with 1 tablespoon yogurt and 1 1/2 teaspoons dill.