To a large pot add the beef broth. Thinly slice the carrots into rounds, and separate the whites of the scallions from their green tops. Chop the white part of the scallions into 1-inch chunks. Reserve the green tops for garnish. Add the sliced carrots and white scallion to the broth. Slice garlic very thin, and grate ginger; add both to the broth. Add the tamari, fish sauce, agave and Sriracha to the pot. Bring the liquid up to a simmer, and lower the heat and simmer the broth for 10 minutes.
Add the lime juice, thinly sliced beef, chopped bok choy, broccoli rabe, mushrooms, and instant ramen noodles to the pot. Simmer gently for 4-5 more minutes. Turn off the heat, cover the pot with a lid, and let the soup rest for 5 minutes.
Thinly slice the green tops of the scallion. Serve the ramen ladled into bowls, topped with scallion and half of a hard boiled egg per bowl.