Start by cooking the quinoa. Combine the quinoa, chicken broth, and water in a sauce pan, bring it to a simmer, cover with a lid, and let slowly simmer for 20 minutes, until the water has been absorbed and the quinoa is fluffy.
While the quinoa is cooking, prepare the sauce for the beef and broccoli. Whisk the soy sauce, corn starch, garlic, sesame oil, sriracha, honey, red wine, and beef broth together.
Heat ⅓ cup of the sauce in a wok or skillet over medium heat. Once hot, add the beef. Use a wooden spoon to break the beef up into small pieces. Let cook for 4 minutes, stirring constantly. Then remove the beef and set aside.
Add another ⅓ cup of the sauce to the wok or skillet. Then add the carrots and mushrooms, and let cook for 3 minutes, stirring frequently. Add the broccoli and let cook for another 3 minutes.
Return the beef to the wok or skillet, add the remaining sauce, and the peas. Let cook for another 5 minutes.
Fluff the quinoa with a fork, and serve the beef and broccoli over the quinoa.