Once oil is hot, add half of the chicken, and cook stirring frequently, until chicken is is golden brown and has cooked through, about 5 minutes. 

Transfer chicken to a plate and add another 1/2 Tbsp vegetable oil to skillet. Cook remaining chicken until golden brown and cooked through, then transfer to plate with first batch of chicken.

In a mixing bowl (or liquid measuring cup used to measure chicken broth), whisk together chicken broth, hoisin sauce, soy sauce, rice vinegar, honey, sesame oil and remaining 2 tsp cornstarch until well blended, set aside.

Heat remaining 1 1/2 Tbsp oil in skillet over medium heat. Add in green onions, garlic, ginger, broccoli and bell pepper and saute until veggies are tender, about 3 minutes. Transfer to a large plate. 

Pour in hoisin sauce mixture and cook, whisking constantly, until sauce boils and thickens (don't let it reduce it will be too salty, just cook long enough to thicken). Thin with 1 - 2 more tablespoons of broth or water if desired.