Prepare noodles according to package directions; drain and set aside.
Heat a non-stick pan over medium-high heat. Add the beef, garlic, and ginger. Sauté breaking the beef up into smaller pieces until no longer pink.
Add the broth, soy sauce, and lime juice. Turn down the heat and bring to a simmer. Add in the broccoli and carrots, cover with a lid and simmer until tender. Toss in the noodles. (Taste and adjust the seasoning with more lime juice or salt.)