Place noodles in a large bowl. Cover with boiling water, and let stand 10 minutes. Drain.
Combine 4 cups water and next 5 ingredients in a large saucepan. Bring to a boil; reduce heat, and simmer, uncovered, 20 minutes. Strain mixture through a sieve into a bowl. Discard solids.
Return broth mixture to pan. Bring to a boil. Add rice noodles; cook 4 minutes. Add steak; reduce heat, and simmer 1 minute. Remove from heat. Stir in green onions and next 3 ingredients. Top each serving evenly with basil and lime juice.