In a medium bowl, combine all the ingredients for the sauce. Taste and adjust seasoning if needed, being cautious with salt.
Place the sliced steak in a large bowl and add half of the marinade. Massage the marinade into the beef and let it marinate for 20 minutes.
Bring a medium pot of water to a boil and cook the noodles according to package instructions. Save the seasoning for another use.
In a large pot over medium-high heat, add 1 tbsp of oil and cook the beef in batches for 1-2 minutes per side. Remove cooked beef and continue until all beef is cooked.
Add another tablespoon of oil to the pot and sauté the onions and broccoli for 2-3 minutes.
Add the cooked noodles and the remaining sauce to the pot with the onions and broccoli. Toss and cook for another 1-2 minutes.
Turn off the heat and add the cooked steak along with any juices from the bowl. Toss everything together.
Serve topped with sliced green onions and sesame seeds. Enjoy!