Combine all of the sauce ingredients in a bowl and whisk to combine. set aside.
In a large skillet or wok, heat 2 tbsp. olive oil and 1 tbsp. sesame oil over medium-high heat.
Season the chicken with salt and pepper, and sear on both sides in the oil until golden brown and cooked through, about 3 minutes per side. Using tongs, transfer the cooked chicken onto a plate and set aside.
Add the bell pepper, onion and broccoli to the skillet and saute for 4 minutes (if for some reason your skillet is looking dry after cooking your chicken, add 1 more tbsp. of olive oil).
Add in the cabbage, carrots, and mushrooms into the skillet. Season with a little salt and pepper and toss until veggie mixture is evenly combined, sauté cabbage until it slightly wilts, about 3 minutes.
Pour in chicken broth and whisk the sauce once more and add the sauce. Toss until cabbage are fully coated and let cook until sauce thickens, about 4 more minutes.
Add chicken back into the dish, the toasted sesame seeds, salt and pepper to taste, and more crushed red pepper if you want it spicier (like me!)
Enjoy!