Prep the chicken and veggies. Slice the chicken into thin strips.
Chop the broccoli, mushrooms, and bell pepper. Mince garlic and grate ginger. Keep everything close—this moves fast.
Make the teriyaki mix. In a bowl, whisk soy sauce, honey (or sugar), vinegar, mirin (if using), chicken broth, water, garlic, ginger, and red pepper flakes.
If you want a slightly glossier broth, whisk cornstarch into the mixture until smooth.
Sear the chicken. Heat oil in a large pot or Dutch oven over medium-high. Season chicken lightly with salt and pepper. Add to the pot in a single layer and cook 3–4 minutes, stirring once or twice, until lightly browned and just cooked through.
Remove to a plate.
Sauté the mushrooms and peppers. In the same pot, add a touch more oil if needed. Cook mushrooms and bell pepper for 2–3 minutes until they start to soften and pick up the browned bits.
Add the teriyaki mix. Pour in the prepared sauce. Bring to a strong simmer, scraping the bottom to release any flavorful bits.
Taste and adjust sweetness or saltiness if needed.
Simmer the noodles. Add the ramen bricks and broccoli. Press them into the liquid. Cook 2–3 minutes, gently loosening the noodles as they soften.
You want them just tender, not mushy.
Return the chicken. Stir the chicken back into the pot. Simmer 1 more minute so everything is hot and coated. If it looks too thick, splash in a little water.
If too thin, simmer another minute uncovered.
Finish and garnish. Turn off heat. Stir in green onions and a drizzle of toasted sesame oil. Top with sesame seeds and an extra scatter of green onions.
Serve with lime wedges if you like a bright pop.