Fill a large soup pot with 7 quarts of water. Add in the beef, onion, carrot, and garlic heads with the skin kept on. Let it simmer for about 90 minutes.
Strain the broth through a cheesecloth. Cut the beef into bite-sized pieces and set them aside.
Place the strained beef broth back into a large soup pot. Dice the asparagus and green onions and add them to the broth, followed by the beef.
Dice the mushrooms and sauté them in a skillet over medium heat until golden brown.
Add the mushrooms into the soup pot and bring the soup to a boil. Pop the rice noodles in and remove the soup from heat.