Heat one Tbsp the olive oil in a large nonstick skillet or a wok over medium-high heat. Add the chicken and cook, stirring, until lightly browned and just cooked through, 5-7 minutes. Stir in ½ a bottle of TERIYAKI SAUCE. Remove the chicken from the skillet and place in a large bowl.
Add the second Tbsp of the olive oil to the skillet and increase the heat to high. Add the shallots, broccoli, mushrooms and the red pepper and cook, stirring constantly until cooked through and lightly browned, about 15 minutes. Stir in the remaining TERIYAKI SAUCE. Lower heat to low. (If you don’t have an extra large pan or wok, cook the vegetables in batches so they brown and don’t steam).
While cooking the vegetables, bring a large pot of salted water to a boil and cook noodles according to their package directions. Drain well and add the noodles to the vegetables. Return heat to medium and return the chicken to the pan. Stir until everything is warmed through, adding more TERIYAKI SAUCE as needed.
Top with scallions and sesame seeds and serve immediately.