Whisk together the soy sauce and cornstarch until smooth. Add 1/4 c beef stock, rice vinegar, brown sugar, and garlic and mix well.
Heat remaining beef stock (not boiling). Put ramen in a pot and add enough beef stock just to cover noodles. Set it aside to let the noodles soften.
While noodles soak, toss with some salt and pepper.
Heat a wok or non-stick pan over medium-high heat. Add 1 Tbsp oil and then the beef. Saute until cooked through, 4 to 5 minutes. Set aside.
Return wok to medium-high heat. Add 1 Tbsp oil and then broccoli. Saute broccoli until it turns bright green and then continue cooking until broccoli is tender (if using frozen broccoli, just saute it until it's heated through and the excess water cooks off). Add in mushrooms.
Add sauce to the pan and toss to coat broccoli and mushrooms. Continue cooking until sauce reduces slightly, 1 to 2 minutes.
Add beef to the pan and toss everything to coat in sauce.
Remove the noodles from the broth, and divide into 4 bowls.
top the noodles with the steak, broccoli and mushrooms.
Ladle about 1/2-3/4 c of broth over the top. Garnish with green onions and a sprinkle of sesame seeds.
For a more authentic experience, add 1/2 of a soft-boiled or poached egg to the garnish step.