Trim fat from beef and discard. Cut beef into 1 ½-inch pieces. In a 6-quart heavy pot cook half the beef in 1 tablespoon of the oil over medium-high heat for 6 to 8 minutes or until beef pieces are well browned, stirring occasionally. Turn heat down to medium if you feel beef is browning too quickly.
Using a slotted spoon, remove beef from pot. Add remaining oil, remaining half of beef and the onion to the same pot. Cook 6 to 8 minutes or until beef is well browned, stirring occasionally.
Add all beef back to pot along with water, broth, and coconut aminos. Bring to boiling; reduce heat. Simmer, covered, for 40 to 45 minutes or until beef is tender.
Meanwhile, peel the carrot. Trim off ends of carrot and discard. Using a vegetable peeler, make long, very thin strips of carrot by peeling the carrot. Turn carrot occasionally so you peel the carrot evenly. When you can no longer get good strips off the carrot, stop peeling. Place the long strips of carrot in a bowl and set aside.
Thinly slice the remaining part of the carrot that you didn’t peel. Remove and discard the piece of ginger from the beef mixture. Add the thinly sliced carrot, the broccoli, chopped ginger, and crushed red pepper (if using) to the pot with beef. Bring to boiling; reduce heat. Simmer, uncovered, for 4 minutes.
Stir the very thin carrot strips into the beef mixture. Cook, uncovered, for 2 minutes.
To serve, ladle beef mixture into shallow bowls. If desired, add noodles or rice to bowls. Sprinkle with cilantro and/or sesame seeds if desired.