In a food processor, add in all ingredients for the sauce. Process until smooth. The sauce should have a thin consistency. If this is not the case, add in one tablespoon of milk and process again. Continue until the desired consistency is reached. Set the sauce aside.
Cook noodles according to package directions and set aside.
In a medium bowl, combine the sesame oil, soy sauce, rice vinegar, brown sugar, and garlic. Add in the sliced beef and toss until fully coated.
Heat a large wok or frying pan over medium-high heat. Add in the beef. Cook for 3-4 minutes or until fully cooked. Transfer the beef to a bowl and set aside.
Heat the same wok or pan over medium heat. Add in the broccoli, carrots, mushrooms, and a splash of water. Cover and cook for 4-6 minutes or until the vegetables are tender.
Add in the beef, noodles, and sauce. Toss until everything is coated in sauce and thoroughly heated.
Divided the stir-fry between four bowls. Garnish with green onions and chopped peanuts. Enjoy!